agent_ui: Fix `context_server` duplication when name is updated (#35403)

Closes #35400

| Before | After |
|--------|--------|
| <video
src="https://github.com/user-attachments/assets/6aae34ca-e022-457a-9b66-47b85c976b23"/>
| <video
src="https://github.com/user-attachments/assets/ae058988-8f70-4605-b537-e045175d2e75"
/> |

Release Notes:

- agent: Fix `context_server` duplication when name is updated

---------

Signed-off-by: Umesh Yadav <git@umesh.dev>
Co-authored-by: Ben Brandt <benjamin.j.brandt@gmail.com>
b35959f4c2Umesh Yadav committed on 9/8/2025, 4:50:26 AM· committed by GitHubparent9450bca
1 file changedLine totals unavailable