Partially closes #39271

Regressed in https://github.com/zed-industries/zed/pull/35375

<img width="282" height="188" alt="image"
src="https://github.com/user-attachments/assets/7e39d819-458a-47a1-96ca-e29797602e73"
/>

Release Notes:

- Fixed the top-right dropdown not showing when you're not signed in.