Data path "" must have required property 'project'.

### Command

generate

### Is this a regression?

- [X] Yes, this behavior used to work in the previous version

### The previous version in which this bug was not present was

_No response_

### Description

Hi

We have two projects that use Angular and Angular CLI. After we've upgraded both projects to Angular 16.x we can't use schematics for one of the projects (second project is fine).
We tried to clear node_modules or cache folders but it didn't help.

### Minimal Reproduction

Any time we try to use schematics we always receive an error:

`ng generate class Test`

### Exception or Error

```text
Schematic input does not validate against the Schema: {"name":"Test","path":"src/app/model"}
Errors:

Data path "" must have required property 'project'.
```

### Your Environment

```text
Angular CLI: 16.1.0
Node: 20.3.0 (Unsupported)
Package Manager: yarn 3.5.1
OS: win32 x64

Angular: 16.1.1
... animations, cdk, common, compiler, compiler-cli, core, forms
... google-maps, localize, material, platform-browser
... platform-browser-dynamic, router

Package Version
---------------------------------------------------------
@angular-devkit/architect 0.1601.0
@angular-devkit/build-angular 16.1.0
@angular-devkit/core 16.1.0
@angular-devkit/schematics 16.1.0
@angular/cli 16.1.0
@schematics/angular 16.1.0
rxjs 7.8.1
typescript 5.0.4
```

### Anything else relevant?

_No response_

Reproduce the reported `ng generate class Test` command in the Angular CLI 16.1.0 environment described and inspect the schematic validation error requiring `project`. Compare the failing project's setup with the working project; done means class generation succeeds without the schema error.

Written by the indexing model from the issue text.