Index type distributes over intersections too eagerly

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### 🔎 Search Terms

index keyof indexed access deferred deferral instantiation

### 🕗 Version & Regression Information

- This is the behavior in every version I tried

### ⏯ Playground Link

https://www.typescriptlang.org/play/?ts=5.8.0-dev.20250202#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-hheppEC41UQPFk2SORE3x5VEFkc5zXPcyAvJ8vyIFgkrl2i6QUPQngsJw05xJeKTrGgcjBFEBjOEubQEBAGj6WLD9aMYIA

### 💻 Code

```ts
type Values = T[keyof T];

// transforms from "keyed object map" to a union
type ExtractEventsFromPayloadMap = Values<{
[K in keyof T]: T[K] & { type: K };
}>;

type EnqueueObject = {
// creates proxy methods
emit: {
[K in TEmittedEvent["type"]]: (
payload: Omit,
) => void;
};
};

type Exec = (
enq: EnqueueObject,
) => void;

declare function createStore(definition: {
emits: {
[K in keyof TEmitted]: (payload: TEmitted[K]) => void;
};
exec: Exec>;
}): any;

createStore({
emits: {
increased: (_: { upBy: number }) => {},
decreased: (_: { downBy: number }) => {},
},
exec: (enq) => {
enq.emit.increased({
upBy: "bazinga", // this should error!
});

const fn = enq.emit.increased;
// ^?

// this is just a copy of what is displayed as `enq.emit.increased`'s type
const exactSameTypeAsAbove: (
payload: Omit<
{ upBy: number } & { type: "increased" } & { type: "increased" },
"type"
>,
) => void = () => {};

exactSameTypeAsAbove({
upBy: "bazinga", // this one errors correctly
});
},
});
```

### 🙁 Actual behavior

There is no error on the annotated call

### 🙂 Expected behavior

It should error

### Additional information about the issue

1. `keyof (T & { type: K })` gets normalized to `keyof T & "type"`
2. that passed through `Exclude` (within `Omit`) is left as `Exclude`.
3. then `T` gets instantiated with `ExtractEventsFromPayloadMap<{ increased: { upBy: number; }; decreased: { downBy: number; }; }`
4. but now `keyof ...` returns only *shared* keys of this **union**
5. the only shared key is `type` so this `Exclude` gets computed as `never` (`Exclude<"type", "type">`)
6. and the final parameter type of `enq.emit.increased` gets computed as just `{}` (from `{ [K in never]: ... }`)

Comienza con la reproducción enlazada de TypeScript Playground y sigue la ruta del checker para indexed access, keyof, intersections y Omit. Compara la llamada al callback anotada con el tipo de función equivalente escrito explícitamente. Se considera terminado cuando la llamada inferida enq.emit.increased rechaza un string para upBy, con una prueba de regresión que cubra el caso reportado.

Escrito por el modelo de indexación a partir del texto del issue.