agent_ui: Fix signed-in check in Zed provider configuration (#36639)

This PR fixes the check for if the user is signed in in the Agent panel
configuration.

Supersedes https://github.com/zed-industries/zed/pull/36634.

Release Notes:

- Fixed the user's plan badge near the Zed provider in the Agent panel
not showing despite being signed in.
c20233e0b4Marshall Bowers committed on 8/20/2025, 11:09:09 PM· committed by GitHubparentffb9951
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