Desktop: Fix search markers vanish when moving focus to a secondary window

[personalizedrefrigerator]

Summary

Previously, highlighted search terms would vanish when moving focus from the primary to a secondary window. With this change, secondary windows continue to highlight the search terms from the primary window, when selected.

Follow-up to a change that mostly resolved #13399.

Screen recording

Screencast.from.2025-12-16.16-21-06.webm

The above screen recording shows:

• Moving focus between multiple windows.
  • The highlighted search terms remain the same.
• Changing the search query from the main window.
  • The highlighted search terms update in the secondary windows and the main window.