Split server/index.js into one file per area

Routes move to server/routes/ (auth, account, projects, reader, sharing, admin);
index.js keeps setup only. A smoke test walks 90 API calls against the real
server and compares every status with the pre-split behaviour.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

TODO.md

@@ -11,7 +11,7 @@ Ideas for the app that haven't been built yet, roughly in the order I'd do them.
       "restore a snapshot" button (snapshots already exist under `DATA_DIR/backups`).
 - [ ] **Checks on every push.** Run tests and lint on the Gitea server, plus a few real-browser tests (Playwright) for sign-in,
       creating a study and syncing; so far everything is tested in simulation.
-- [ ] **Split `server/index.js`** (now about 1,100 lines) into one file per area (auth, projects, sharing, reader data, admin).
+- [x] **Split `server/index.js`** into one file per area (`server/routes/`: auth, account, projects, reader, sharing, admin).
 
 ## Teaching together
 - [ ] **Comments between co-teachers.** Notes on a chunk addressed to the other person, instead of editing each other's text.