Remove the old backend, sync layer and dropped pages

[paccloud]

What to build

Once the app runs on Firebase, delete what the switch made unnecessary, following ADRs 0001 and 0003 in #122:

• the old backends: api/, server/, shared/, SQLite, the Neon client and the legacy password login
• the custom sync layer, conflict screen, old guest storage and guest adoption code
• the pages that are not among the five (Calculator, My data, Community, About, Review): for example Upload, Submit request, Data sources, Profile and Roadmap

Update CLAUDE.md, the README and the deployment docs to describe the new setup, including dropping the rule to change both backends. Superseded docs (such as docs/AUTH_MIGRATION_ROADMAP.md) are removed or marked superseded.

Acceptance criteria

• api/, server/, shared/, the SQLite and Neon code, the legacy login, the sync layer and the guest adoption code are gone
• The app has only the five pages; old paths redirect to the closest remaining page
• Dependencies used only by removed code are removed
• CLAUDE.md, the README and the deployment docs describe Firebase Auth, Firestore, Hosting and the emulators
• Lint, tests and the build pass

Blocked by

• Sign in with an email link #124
• Guests save with anonymous sign-in and keep their data on sign-in #125
• Import custom yields from Excel/CSV in the browser #127
• Community page with CSV/JSON download #129
• Serve from Firebase Hosting and redirect the Vercel address #132