Add folder move functionality to browse tab

[tnswo561412]

Summary

• Add ability to move entire folders (including subfolders and notes) to a different location
• Long-press a folder in the Browse tab to access the new "Move" button
• Dialog allows browsing and selecting destination folder
• Automatically handles name conflicts by appending a number suffix
• Prevents invalid moves (e.g., moving a folder into itself)

Test plan

• Long-press a folder and verify the move icon appears between rename and delete
• Tap move icon and verify destination picker dialog opens
• Navigate to different folders within the dialog
• Move a folder to a new location and verify all contents are preserved
• Attempt to move a folder into its own subfolder and verify error message
• Move a folder to a location with a same-named folder and verify auto-rename

[tnswo561412]

I understand you must be busy, but I would highly appreciate it if you could spare some time to review this PR. As a part of a university course assignment, feedback or a merge is crucial for my submission deadline.

Please let me know if there are any issues I need to resolve, or if you have specific feedback on the code. Thank you for your time!

[ChromiumOS-Guy]

#1540 this needs solving please review this merge.