Add beta menu to the agentic sidebar

[shaunandrews]

Related issues

• None

How AI was used in this PR

AI assisted with implementation, iterative UI refinement, test coverage, and verification. The final behavior and visual treatment were reviewed interactively in the desktop app.

Proposed Changes

• Add a compact BETA affordance above Settings so people can identify the agentic Studio experience without competing with sidebar messages or onboarding tasks.
• Let people switch back to Studio Classic or send feedback from an anchored menu.
• Show the running Studio version in the menu to make feedback and troubleshooting more useful.
• Keep the affordance accessible with stable filled active states and an offset keyboard-focus outline.

Testing Instructions

1. Start Studio with the agentic UI enabled.
2. Confirm the BETA badge appears above Settings and does not overlap sidebar messages.
3. Open the badge menu and verify “Switch to Studio Classic,” “Send feedback,” and the current Studio version.
4. Verify the badge remains blue while the menu is open and shows an offset outline for keyboard focus.
5. Check both light and dark appearance modes.

Screenshots

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?