The type definition of $ref not correctly resolve

**What version of Ajv are you using? Does the issue happen if you use the latest version?**
8.8.2, yes
**Your typescript code**

```typescript
import Ajv, { JSONSchemaType } from "ajv";
const ajv = new Ajv({
allErrors: true,
});

interface EventChainJSON {
[key: string]: EventChain;
}

interface EventChain {
main: AtomicEvent;
[key: string]: AtomicEvent;
}

interface AtomicEvent {
type: string;
version?: string;
params?: { [key: string]: any };
callback?: { [key: string]: NextEvent };
next?: NextEvent;
}

type NextEvent = AtomicEvent | string;

const schema: JSONSchemaType & {
definitions: {
ec: JSONSchemaType;
ae: JSONSchemaType;
ne: JSONSchemaType;
};
} = {
definitions: {
ec: {
type: "object",
properties: {
main: { $ref: "#/definitions/ae" },
},
additionalProperties: { $ref: "#/definitions/ae" },
},
ae: {
type: "object",
properties: {
type: { type: "string" },
version: { type: "string" },
params: { type: "object" },
callback: {
type: "object",
additionalProperties: {
$ref: "#/definitions/ne",
},
},
next: {
$ref: "#/definitions/ne",
},
},
required: ["type"],
additionalProperties: false,
},
ne: {
anyOf: [{ type: "string" }, { $ref: "#/definitions/ae" }],
},
},
type: "object",
additionalProperties: { $ref: "#/definitions/ec" },
};
```

**Typescript compiler error messages**

```
TSError: ⨯ Unable to compile TypeScript:
ajv.ts:33:5 - error TS2322: Type '{ type: "object"; properties: { main: { $ref: string; }; }; additionalProperties: { $ref: string; }; }' is not assignable to type 'UncheckedJSONSchemaType'.
Types of property 'additionalProperties' are incompatible.
Type '{ $ref: string; }' is not assignable to type 'boolean | UncheckedJSONSchemaType | undefined'.
Type '{ $ref: string; }' is not assignable to type '{ type: "object"; additionalProperties?: boolean | UncheckedJSONSchemaType | undefined; unevaluatedProperties?: boolean | UncheckedJSONSchemaType | undefined; ... 7 more ...; maxProperties?: number | undefined; } & { ...; } & { ...; } & { ...; }'.
Property 'type' is missing in type '{ $ref: string; }' but required in type '{ type: "object"; additionalProperties?: boolean | UncheckedJSONSchemaType | undefined; unevaluatedProperties?: boolean | UncheckedJSONSchemaType | undefined; ... 7 more ...; maxProperties?: number | undefined; }'.

33 ec: {
~~

node_modules/ajv/dist/types/json-schema.d.ts:57:5
57 type: JSONType<"object", IsPartial>;
~~~~
'type' is declared here.
ajv.ts:27:5
27 ec: JSONSchemaType;
~~
The expected type comes from property 'ec' which is declared here on type 'Record> & { ec: UncheckedJSONSchemaType; ae: UncheckedJSONSchemaType<...>; ne: UncheckedJSONSchemaType<...>; }'
ajv.ts:40:5 - error TS2322: Type '{ type: "object"; properties: { type: { type: "string"; }; version: { type: "string"; }; params: { type: "object"; }; callback: { type: "object"; additionalProperties: { $ref: string; }; }; next: { $ref: string; }; }; required: "type"[]; additionalProperties: false; }' is not assignable to type 'UncheckedJSONSchemaType'.
The types of 'properties.version' are incompatible between these types.
Type '{ type: "string"; }' is not assignable to type '{ $ref: string; } | (UncheckedJSONSchemaType & { nullable: true; const?: null | undefined; enum?: readonly (string | null | undefined)[] | undefined; default?: string | ... 1 more ... | undefined; })'.
Type '{ type: "string"; }' is not assignable to type '{ type: "string"; } & StringKeywords & { allOf?: readonly UncheckedPartialSchema[] | undefined; anyOf?: readonly UncheckedPartialSchema[] | undefined; ... 4 more ...; not?: UncheckedPartialSchema<...> | undefined; } & { ...; } & { ...; }'.
Property 'nullable' is missing in type '{ type: "string"; }' but required in type '{ nullable: true; const?: null | undefined; enum?: readonly (string | null | undefined)[] | undefined; default?: string | null | undefined; }'.

40 ae: {
~~

node_modules/ajv/dist/types/json-schema.d.ts:115:5
115 nullable: true;
~~~~~~~~
'nullable' is declared here.
ajv.ts:28:5
28 ae: JSONSchemaType;
~~
The expected type comes from property 'ae' which is declared here on type 'Record> & { ec: UncheckedJSONSchemaType; ae: UncheckedJSONSchemaType<...>; ne: UncheckedJSONSchemaType<...>; }'
ajv.ts:59:5 - error TS2322: Type '{ anyOf: ({ type: "string"; } | { $ref: string; })[]; }' is not assignable to type 'UncheckedJSONSchemaType'.
Type '{ anyOf: ({ type: "string"; } | { $ref: string; })[]; }' is not assignable to type '{ type: "string"; } & StringKeywords & { allOf?: readonly UncheckedPartialSchema[] | undefined; anyOf?: readonly UncheckedPartialSchema[] | undefined; ... 4 more ...; not?: UncheckedPartialSchema<...> | undefined; } & { ...; }'.
Property 'type' is missing in type '{ anyOf: ({ type: "string"; } | { $ref: string; })[]; }' but required in type '{ type: "string"; }'.

59 ne: {
~~

node_modules/ajv/dist/types/json-schema.d.ts:31:5
31 type: JSONType<"string", IsPartial>;
~~~~
'type' is declared here.
ajv.ts:29:5
29 ne: JSONSchemaType;
~~
The expected type comes from property 'ne' which is declared here on type 'Record> & { ec: UncheckedJSONSchemaType; ae: UncheckedJSONSchemaType<...>; ne: UncheckedJSONSchemaType<...>; }'

at createTSError (/usr/local/lib/node_modules/ts-node/src/index.ts:750:12)
at reportTSError (/usr/local/lib/node_modules/ts-node/src/index.ts:754:19)
at getOutput (/usr/local/lib/node_modules/ts-node/src/index.ts:941:36)
at Object.compile (/usr/local/lib/node_modules/ts-node/src/index.ts:1243:30)
at Module.m._compile (/usr/local/lib/node_modules/ts-node/src/index.ts:1370:30)
at Module._extensions..js (node:internal/modules/cjs/loader:1153:10)
at Object.require.extensions. [as .ts] (/usr/local/lib/node_modules/ts-node/src/index.ts:1374:12)
at Module.load (node:internal/modules/cjs/loader:981:32)
at Function.Module._load (node:internal/modules/cjs/loader:822:12)
at Function.executeUserEntryPoint [as runMain] (node:internal/modules/run_main:79:12) {
diagnosticText: `\x1B[96majv.ts\x1B[0m:\x1B[93m33\x1B[0m:\x1B[93m5\x1B[0m - \x1B[91merror\x1B[0m\x1B[90m TS2322: \x1B[0mType '{ type: "object"; properties: { main: { $ref: string; }; }; additionalProperties: { $ref: string; }; }' is not assignable to type 'UncheckedJSONSchemaType'.\n` +
" Types of property 'additionalProperties' are incompatible.\n" +
" Type '{ $ref: string; }' is not assignable to type 'boolean | UncheckedJSONSchemaType | undefined'.\n" +
` Type '{ $ref: string; }' is not assignable to type '{ type: "object"; additionalProperties?: boolean | UncheckedJSONSchemaType | undefined; unevaluatedProperties?: boolean | UncheckedJSONSchemaType | undefined; ... 7 more ...; maxProperties?: number | undefined; } & { ...; } & { ...; } & { ...; }'.\n` +
` Property 'type' is missing in type '{ $ref: string; }' but required in type '{ type: "object"; additionalProperties?: boolean | UncheckedJSONSchemaType | undefined; unevaluatedProperties?: boolean | UncheckedJSONSchemaType | undefined; ... 7 more ...; maxProperties?: number | undefined; }'.\n` +
'\n' +
'\x1B[7m33\x1B[0m ec: {\n' +
'\x1B[7m \x1B[0m \x1B[91m ~~\x1B[0m\n' +
'\n' +
' \x1B[96mnode_modules/ajv/dist/types/json-schema.d.ts\x1B[0m:\x1B[93m57\x1B[0m:\x1B[93m5\x1B[0m\n' +
' \x1B[7m57\x1B[0m type: JSONType<"object", IsPartial>;\n' +
' \x1B[7m \x1B[0m \x1B[96m ~~~~\x1B[0m\n' +
" 'type' is declared here.\n" +
' \x1B[96majv.ts\x1B[0m:\x1B[93m27\x1B[0m:\x1B[93m5\x1B[0m\n' +
' \x1B[7m27\x1B[0m ec: JSONSchemaType;\n' +
' \x1B[7m \x1B[0m \x1B[96m ~~\x1B[0m\n' +
" The expected type comes from property 'ec' which is declared here on type 'Record> & { ec: UncheckedJSONSchemaType; ae: UncheckedJSONSchemaType<...>; ne: UncheckedJSONSchemaType<...>; }'\n" +
`\x1B[96majv.ts\x1B[0m:\x1B[93m40\x1B[0m:\x1B[93m5\x1B[0m - \x1B[91merror\x1B[0m\x1B[90m TS2322: \x1B[0mType '{ type: "object"; properties: { type: { type: "string"; }; version: { type: "string"; }; params: { type: "object"; }; callback: { type: "object"; additionalProperties: { $ref: string; }; }; next: { $ref: string; }; }; required: "type"[]; additionalProperties: false; }' is not assignable to type 'UncheckedJSONSchemaType'.\n` +
" The types of 'properties.version' are incompatible between these types.\n" +
` Type '{ type: "string"; }' is not assignable to type '{ $ref: string; } | (UncheckedJSONSchemaType & { nullable: true; const?: null | undefined; enum?: readonly (string | null | undefined)[] | undefined; default?: string | ... 1 more ... | undefined; })'.\n` +
` Type '{ type: "string"; }' is not assignable to type '{ type: "string"; } & StringKeywords & { allOf?: readonly UncheckedPartialSchema[] | undefined; anyOf?: readonly UncheckedPartialSchema[] | undefined; ... 4 more ...; not?: UncheckedPartialSchema<...> | undefined; } & { ...; } & { ...; }'.\n` +
` Property 'nullable' is missing in type '{ type: "string"; }' but required in type '{ nullable: true; const?: null | undefined; enum?: readonly (string | null | undefined)[] | undefined; default?: string | null | undefined; }'.\n` +
'\n' +
'\x1B[7m40\x1B[0m ae: {\n' +
'\x1B[7m \x1B[0m \x1B[91m ~~\x1B[0m\n' +
'\n' +
' \x1B[96mnode_modules/ajv/dist/types/json-schema.d.ts\x1B[0m:\x1B[93m115\x1B[0m:\x1B[93m5\x1B[0m\n' +
' \x1B[7m115\x1B[0m nullable: true;\n' +
' \x1B[7m \x1B[0m \x1B[96m ~~~~~~~~\x1B[0m\n' +
" 'nullable' is declared here.\n" +
' \x1B[96majv.ts\x1B[0m:\x1B[93m28\x1B[0m:\x1B[93m5\x1B[0m\n' +
' \x1B[7m28\x1B[0m ae: JSONSchemaType;\n' +
' \x1B[7m \x1B[0m \x1B[96m ~~\x1B[0m\n' +
" The expected type comes from property 'ae' which is declared here on type 'Record> & { ec: UncheckedJSONSchemaType; ae: UncheckedJSONSchemaType<...>; ne: UncheckedJSONSchemaType<...>; }'\n" +
`\x1B[96majv.ts\x1B[0m:\x1B[93m59\x1B[0m:\x1B[93m5\x1B[0m - \x1B[91merror\x1B[0m\x1B[90m TS2322: \x1B[0mType '{ anyOf: ({ type: "string"; } | { $ref: string; })[]; }' is not assignable to type 'UncheckedJSONSchemaType'.\n` +
` Type '{ anyOf: ({ type: "string"; } | { $ref: string; })[]; }' is not assignable to type '{ type: "string"; } & StringKeywords & { allOf?: readonly UncheckedPartialSchema[] | undefined; anyOf?: readonly UncheckedPartialSchema[] | undefined; ... 4 more ...; not?: UncheckedPartialSchema<...> | undefined; } & { ...; }'.\n` +
` Property 'type' is missing in type '{ anyOf: ({ type: "string"; } | { $ref: string; })[]; }' but required in type '{ type: "string"; }'.\n` +
'\n' +
'\x1B[7m59\x1B[0m ne: {\n' +
'\x1B[7m \x1B[0m \x1B[91m ~~\x1B[0m\n' +
'\n' +
' \x1B[96mnode_modules/ajv/dist/types/json-schema.d.ts\x1B[0m:\x1B[93m31\x1B[0m:\x1B[93m5\x1B[0m\n' +
' \x1B[7m31\x1B[0m type: JSONType<"string", IsPartial>;\n' +
' \x1B[7m \x1B[0m \x1B[96m ~~~~\x1B[0m\n' +
" 'type' is declared here.\n" +
' \x1B[96majv.ts\x1B[0m:\x1B[93m29\x1B[0m:\x1B[93m5\x1B[0m\n' +
' \x1B[7m29\x1B[0m ne: JSONSchemaType;\n' +
' \x1B[7m \x1B[0m \x1B[96m ~~\x1B[0m\n' +
" The expected type comes from property 'ne' which is declared here on type 'Record> & { ec: UncheckedJSONSchemaType; ae: UncheckedJSONSchemaType<...>; ne: UncheckedJSONSchemaType<...>; }'\n",
diagnosticCodes: [ 2322, 2322, 2322 ]
}
```

**Describe the change that should be made to address the issue?**
The type definition of $ref should be correctly resolved
**Are you going to resolve the issue?**
no