Markdown Preview search does not work when preview is moved to a separate window

Does this issue occur when all extensions are disabled?: Yes

- VS Code Version: 1.136.1
- OS Version: macOS 26.6.0 (Darwin arm64)

Steps to Reproduce:

1. Open a `.md` file.
2. Open the Markdown Preview using "Open Preview".
3. Move/detach the Markdown Preview tab into a separate VS Code window.
4. Focus the Markdown Preview window.
5. Press `Cmd + F` on macOS or `Ctrl + F` on Linux.
6. Search for a word that exists in the Markdown document.

Expected:
The search should find and highlight the matching text in the Markdown Preview when it is opened in a separate VS Code window.

Actual:
The search does not find or highlight the searched word when the Markdown Preview is in a separate VS Code window.

The same search works correctly when the Markdown Preview remains in the original VS Code window.