docs: push notifications module + FCM client wiring

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

README.md

@@ -83,6 +83,13 @@ client's host - no separate web server is needed.
   `MailService.sendTeamerInvite()` composes the personal-invite email with a
   link built from `APP_BASE_URL`. Delivery is best-effort — failures are
   logged and swallowed, never blocking the invite.
+- `push/` — global `PushProvider` abstraction; default `log`, `PUSH_PROVIDER=fcm`
+  uses FCM HTTP v1 (service-account JWT → OAuth token, no extra dep;
+  `FCM_PROJECT_ID`, `GOOGLE_APPLICATION_CREDENTIALS`). `DeviceToken` rows
+  (bound to a `User` or `GuestAccount`) via `POST /push/register` +
+  `/unregister`. `PushService.notifyChannel()` resolves a channel's readable
+  audience → their tokens (minus the sender) → send, pruning invalid ones;
+  `ChatService.sendMessage()` fires it best-effort.
 - `wahl/` — Wahl/Workshop administration (Leitungsteam-only), guest
   Teilnehmer submission, Force-Zuteilung overrides, and `ZuteilungService`:
   a faithful port of the WP plugin's `kc_run_zuteilung` (force-assignments →
@@ -119,11 +126,11 @@ client's host - no separate web server is needed.
 - `common/` — `Role` enum, `@Roles()` decorator, `RolesGuard` (KC-scoped,
   Leitungsteam roles are global across all KCs).
 
-All planned backend phases are implemented. `npm test` runs Jest unit tests
-(`ZuteilungService`, `TeamAuthService`, `TeamerService`, `OnboardingService`,
+All planned backend features are implemented (`prisma/migrations/` holds the
+schema history). `npm test` runs Jest unit tests (`ZuteilungService`,
+`TeamAuthService`, `TeamerService`, `OnboardingService`,
 `resolveOrProvisionAuthentikUser` / `toAuthenticatedUser`; Prisma mocked).
-Remaining work: the Flutter clients (see repo root README), push
-notifications, and the first real Prisma migration (only `schema.prisma`
-exists so far). Ops notes: the Authentik provider must emit a `groups` claim
-for the LT check, and `MAIL_PROVIDER=smtp` + `SMTP_*` must be set for invite
-emails to actually leave the box.
+Ops notes to go live: the Authentik provider must emit a `groups` claim for
+the LT check; `MAIL_PROVIDER=smtp` + `SMTP_*` for invite emails;
+`PUSH_PROVIDER=fcm` + a Firebase service-account JSON for push; and real
+Nextcloud/S3 credentials for file storage.