Look at the editor hint:

So in fact, this JSDoc does indicate that A is deprecated. Changing it would require changing TS, not us.

Does it? See this code in the TypeScript playground:

namespace A.B {
  /** @deprecated */
  export const x = "x";
  export const y = "y"
}

/** @deprecated */
namespace A.C {
  export const z = "z";
}

console.log(A.B.x);
console.log(A.B.y);

On the two console.log lines, the editor applies the deprecation strikethrough only to the element x, not to either instance of the element A.

The strikethrough seems to be applied inconsistently. Consider:

/** @deprecated */
namespace Foo.Bar {
  export const x = 1;
}

namespace Foo.Baz {
  export const x = 1;
}

Foo.Bar.x;

OTOH, if you reorder Foo.Bar and Foo.Baz, you don't get any strikethroughs, on either Foo or Foo.Baz. Nevertheless, the quickinfo tells you that Foo indeed gets the @deprecated annotation, so it's considered deprecated when we query TS type info.

Yeah I'd agree here.

Your code is really ambiguous.

/** @deprecated */
namespace Foo.Bar {}

What's meant to be deprecated here?
Is it Foo or Foo.Bar or both?
Is there another declaration of Foo that isn't deprecated? Is it supposed to be or is it not?

Add to that what Josh has found -- TS is even unsure what you meant!

So the recommendation is that you need to disambiguate your code.
EG by explicitly nesting the namespace and attaching the deprecation comment appropriately

namespace Foo {
  /** @deprecated */
  export namespace Bar {}
}

Or in the context of your example:

declare namespace A.B {
  const y: string;
}

declare namespace A {
  /** @deprecated */
  namespace C {
    const z: string;
  }
}

console.log(A.B.y); // no error
console.log(A.C.z); // errors

playground

In this case it's from @types/chrome, so I'd appreciate how hard it would be to fix... Could be helped by an ignore option though, like #9899.

Filed microsoft/TypeScript#59792 -- we'll see what they say.
Clarification on the "correct" disambiguation would be good.