Follow up to https://github.com/zed-industries/zed/pull/23299.

Having the loading state on the button makes sense, but it's also too
subtle. If you're waiting on an LLM response that takes a while, like a
"thinking state", not having anything more clearly visible communicating
that the model is still in-progress can make you think something is
wrong.

<img
src="https://github.com/user-attachments/assets/da64516e-5540-4294-97a2-e4542ce704f3"
width="700px" />

Release Notes:

- N/A