Self-Review Checklist:

- [x] I've reviewed my own diff for quality, security, and reliability
- [ ] Unsafe blocks (if any) have justifying comments
- [x] The content is consistent with the [UI/UX
checklist](https://github.com/zed-industries/zed/blob/main/CONTRIBUTING.md#uiux-checklist)
- [ ] Tests cover the new/changed behavior
- [X] Performance impact has been considered and is acceptable

Closes #52064

Release Notes:

- Fixed copy button overlapping code block content in the Agent panel
(#52064)

## Demo

Before:
<img width="496" height="139" alt="image"
src="https://github.com/user-attachments/assets/6c49ad7f-ae36-4a6b-be72-783ff6e98537"
/>
<img width="411" height="182" alt="image"
src="https://github.com/user-attachments/assets/a4b89407-2ae0-4629-875b-706592e81b34"
/>

After:


https://github.com/user-attachments/assets/a139db06-3909-4a22-881a-836262ed3c36