AI Assistant: Search field text overflows and obscures control buttons

Steps to reproduce:

1. Create a Unity project
2. Select "Light" Unity theme
3. Click the "AI" button
4. Click "Agree and install Unity AI"
5. Wait until the installation is complete
6. Open the Assistant window
7. Click the "Search" button, which should be displayed before the "Chats" button
8. Enter a long search string, which would not fit into the field width
9. Observe the result

Actual results: When entering a long string of text into the "Find in conversation" search field, the text does not wrap or truncate. Instead, it continues horizontally, overlapping and eventually completely obscuring the "No results" indicator and the "X" (clear) button.

Expected results: The search field should have a defined text-viewport. Long input strings should either truncate with an ellipsis, scroll horizontally within the field's boundaries, or wrap, ensuring that functional UI elements (like the clear button and results counter) remain visible and interactable at all times.

Reproducible with versions: 2.5.0-pre.2

Tested on (OS): macOS - Tahoe 26.4