Upgrade extension UI for professor ratings and parity investigation

[kleinpanic]

Parent: #43

Design and implement browser extension support for professor/rating context.

Goals

• investigate how close extension UI should track TUI presentation
• define popup UX for rating summaries or drill-down
• route any new runtime messages through the shared extension contract
• keep styling coherent with the refreshed extension architecture

Deliverables

• UX plan
• extension UI implementation
• runtime/client wiring
• parity notes

[kleinpanic]

Verified complete by PR #94 (ext-ui redesign + professor ratings layout). No additional work needed in Phase 8. Closing.