What
---
The keybinding hint in the Project Search status bar button tooltip
disappears shortly after the tooltip appears, while the label "Project
Search" remains. This is most reproducible with no file open.

Why
---
`SearchButton` used `Tooltip::for_action` with no stored focus handle,
so `KeyBinding::render` called `window.focused(cx)` at render time to
resolve the `pane::DeploySearch` binding. When the `Tooltip` entity
re-rendered (it subscribes to theme settings changes) and the focused
element was no longer in a `Pane` key context, the keybinding lookup
failed silently and the shortcut hint vanished.

Fix
---
Store the active pane item's `FocusHandle` in `SearchButton` via
`set_active_pane_item` and use `Tooltip::for_action_in` so the
keybinding is always resolved against a stable `Pane` context. Falls
back to `Tooltip::for_action` when no pane item is active.

Closes #51562

Test Plan
---

- [x] `cargo fmt --check`
- [ ] `cargo test --workspace`
   - currently blocked by an unrelated compile error test 
- tests::test_terminal_kill_allows_wait_for_exit_to_complete ... FAILED
- [x] Manual verification of:
- Try to reproduce the issue and the keyboard shortcut visible for as
long as the cursor is hovering over the button.
   
Release Notes
- Fixed Project Search status bar button tooltip keybinding hint
disappearing while hovering

Screenshots
---
Current:
<img width="835" height="496" alt="image"
src="https://github.com/user-attachments/assets/cb1ffdf2-7733-47f6-9030-041459c2734c"
/>

Expected:
<img width="835" height="496" alt="image"
src="https://github.com/user-attachments/assets/84cb54b9-290c-4210-b86b-7ae9f8bf9ac0"
/>

Release Notes:

- N/A