Add Playwright test for live session control

[rogerSuperBuilderAlpha]

Path: app/api/live/[sessionId]/control/route.ts, app/live/
Size: M

Problem / Context: Live session control (start, pause, end) untested. Could accept invalid state transitions.

Proposed scope:

• Create __tests__/e2e/live-session.spec.ts
• Test: start session, pause, resume, end
• Invalid transitions rejected (e.g., pause before start)
• Auth required (host only)

Acceptance criteria:

• State machine tested (5+ transitions)
• Auth validation covered
• Integration with Firestore verified

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[mrrCarter]

Current develop already has focused live session control coverage without needing a slower e2e duplicate: tests/app/api/live/control/route.test.ts covers auth required, invalid action validation, dispatching valid control actions, and domain error mapping; tests/lib/live-sessions/data-server.test.ts covers the controlLiveSessionServer state machine including start-next, pause/resume, end-session, no queued speakers, unauthorized emcee, and queue mutations; tests/app/live/emcee-page.test.ts covers the emcee UI posting control actions. Skipping a duplicate PR for #588.

[github-actions]

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