input: Fix search feedback loop (#2781)

## Description

The gpui-base refactor accidentally broke the search with a
echo/feedback loop. The query kept getting reset. What was happening:

1. Typing in the search panel fires InputEvent::Change, which writes the
query into the editor's search_session
2. InputOverlayHost::sync runs every frame and compares a signature
(open, replace_mode, query, anchor_offset) to decide whether to re-show
the panel
The panels own write changed the query component, so every keystroke
triggered show_with_focus again
3. show_with_focus runs set_value + select_all, so the next keystroke
replaced the entire query

This fix skips the re-opening like the original code intended.

## Videos

### Before


https://github.com/user-attachments/assets/54d83ff2-983d-473f-a11d-f3c0881a60a0

### After


https://github.com/user-attachments/assets/c594e5a6-a333-4b2f-a378-ff1b1d97a419

## How to Test

Try searching in the editor example

## Checklist

- [x] I have read the [CONTRIBUTING](../CONTRIBUTING.md) document and
followed the guidelines.
- [x] Reviewed the changes in this PR and confirmed AI generated code
(If any) is accurate.
- [x] Passed `cargo run` for story tests related to the changes.
- [ ] Tested macOS, Windows and Linux platforms performance (if the
change is platform-specific)