Removing it for two reasons:

1. We need a better implementation that doesn't hurt caching and doesn't
distracts the agent too much (see
https://github.com/zed-industries/zed/pull/32876 for more context)

2. Current insertion point of notifications doesn't play well with
Claude Thinking models (see
https://github.com/zed-industries/zed/issues/33000#issuecomment-2991709484)

I think we should get this code back in a form of a tool. But for now,
I'm dropping it to resolve recent issues.

Closes #33000

Release Notes:

- N/A