Improve browser extension UX and sync features

[idncsk]

Implement persistent tab selections, add advanced sync filtering options, and introduce context menus for Canvas insertion in both browser and popup.

The selection fixes address user experience issues where selections were unexpectedly cleared after certain tab operations, preventing efficient chained actions. The new sync settings provide users with more control over which tabs are synced, aligning with specific workflow needs. Context menus streamline the process of inserting tabs into Canvas by making the functionality readily accessible from the browser's native tab context and the extension's popup.

---

[cursor]

Cursor Agent can help with this pull request. Just @cursor in comments and I'll start working on changes in this branch.
_{Learn more about Cursor Agents}