assistant panel: Avoid auth prompt on provider switch (#15478)

Previously, the following lead to a bug:

1. Set OpenAI key
2. Switch to Anthropic
3. Restart Zed
4. Switch provider to OpenAI -> get prompted for authentication prompt

With this change, you won't get prompted for the OpenAI key again.

Release Notes:

- N/A

Co-authored-by: Bennet <bennet@zed.dev>