String extends Function?

Question

I ran into a typing problem after upgrading a library. This is the distilled form of the bug:

class Bar {
  id: string = '';
}

declare type ExcludeFunctions<T, K extends keyof T> = T[K] extends Function ? never : (K extends symbol ? never : K);


declare type Baz<T> = {
  [K in keyof T as ExcludeFunctions<T, K>]?: T[K];
};


class Base<T extends Bar> {

  public async foo(input: Baz<T>) {
   //Property 'id' does not exist on type 'Baz<T>'.
    input.id = 'x';
  }
}

Why doesn't Baz have property 'id'? It looks like "string extends Function" evaluates to true, because when I remove this condition the error disappears. But string clearly doesn't extend Function. What is going on here?