fix: sync browsing when entering a directory from filtered view

[veeso]

Summary

• Fixes sync browsing not triggering when entering a directory from a filtered (/) view
• Reuses existing synchronize_browsing logic (including mkdir prompt on the opposite pane) by making it pub(crate)

Closes #382

Test plan

• Enable sync browsing between local and remote with matching directory structures
• Use / to filter directories, enter one, and verify both panes navigate
• Verify normal (non-filtered) sync browsing still works as before
• Verify the mkdir prompt still appears if the directory doesn't exist on the opposite side

[cocogitto-bot]

✔️ 990a05c - Conventional commits check succeeded.