[codex] Add public demo auth and evaluation tooling

[arugo11]

What changed

Preserves the in-progress sit-copilot work from this PC before reset.

Included work

• public demo session bootstrap and rate limiting
• lecture QA auth flow updates and frontend session handling
• Azure deploy/runtime hardening for the students environment
• evaluation scripts, reports, and tests for lecture QA and live caption replay

Why

This branch captures the current demo and evaluation work so it can be reviewed and integrated later without losing the local state on this PC.

Validation

• Passed python3 -m pytest tests/api/v4/test_auth.py tests/unit/evaluation/test_lecture_qa_eval.py tests/unit/evaluation/test_live_caption_replay.py