chore: remove Firebase backend code, replaced by Supabase (see 2026-08-08 spec)

Deleted all Firebase-specific files and directories:
- Configuration: .firebaserc, firebase.json, firestore.* files, storage.rules
- Cloud Functions: functions/ directory (package.json, source, config)
- Tests: firebase-tests/, vitest.rules.config.ts
- Scripts: scripts/seed.ts
- Source: src/lib/firebase.ts and .test.ts
- Environment: .env.example

Removed dependencies:
- firebase (main package)
- firebase-admin, firebase-tools (dev)
- @firebase/rules-unit-testing (dev)

Removed scripts:
- test:rules (Firebase emulator tests)
- seed (Firestore seed script)

Updated package.json via npm install (729 packages removed)
Updated .gitignore (removed functions/ entries)
Updated vite.config.ts (removed firebase-tests and functions exclusions)

All tests, builds, and lints pass cleanly. No Firebase references remain in
the codebase (only in historical spec documents in docs/).

Claude-Session: https://claude.ai/code/session_01NhxA4npAXAxmCDEJt6kxSH

vite.config.ts

@@ -14,8 +14,6 @@ export default defineConfig({
       '**/cypress/**',
       '**/.{idea,git,cache,output,temp}/**',
       '**/{karma,rollup,webpack,vite,vitest,jest,ava,babel,nyc,cypress,tsup,build}.config.*',
-      'firebase-tests/**',
-      'functions/**',
     ],
   },
 })