Fixes
1. popup.js was unconditionally opening the sidebar the instant the popup was opened — even with nothing pending — which is why settings and the sidebar both appeared after install with no way to close the sidebar. Removed that; the sidebar now only opens from an explicit button click.
2. Both extensions' background scripts now fall back to opening the analysis in a new website tab when the sidebar/side panel can't be opened, instead of leaving the user with just a badge and a "go click the toolbar" message. On Firefox this fires every time from that button (expected);
3. Updated the toast/button copy in both languages to reflect "opened in a new tab" instead of the old dead-end hint.

1.0.1 — Compatibility fixes

Switched all extension APIs from Chrome's callback-based chrome. namespace to Firefox's native promise-based browser. namespace. This fixes intermittent failures in context menu registration, tab badge updates (YT/PDF indicators), settings sync, and sidebar opening that could occur because chrome.* is only a compatibility shim in Firefox and doesn't reliably behave like the real API. No new features or permission changes.