Implement push notifications Phase 1 (FCM + project relay)

Backend (Rust):
- push_tokens migration, model (PushToken/PushPlatform), and db layer
  (upsert/list/delete/delete_many)
- PUT/DELETE /api/push_tokens endpoints wired into the router + OpenAPI
- "push" notification method: relay sender (reqwest) that forwards only the
  sanitized title/body and prunes dead tokens, plus settings with a default
  relay_url
- 164 tests pass, clippy clean

Relay (push_relay/, TypeScript Firebase Cloud Function):
- POST /v1/push (firebase-admin sendEach + per-token status mapping),
  GET /healthz, payload validation, per-IP Firestore rate limiting
- Jest tests + README documenting the manual project-owned setup

Frontend (Flutter):
- oott_api_push.dart (register/unregister), push_service.dart behind a
  PushService abstraction, and a per-device push toggle in settings
- firebase_core/firebase_messaging/flutter_local_notifications deps
- 145 tests pass, dart analyze clean

Dev shell:
- add nodejs_22 to the Nix dev shell so the relay tests/build run locally

Remaining (manual, project-owned): create the Firebase project, deploy the
relay and set the real default_relay_url, add native Firebase config, and test
on real devices.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/windows/flutter/generated_plugin_registrant.cc

@@ -8,6 +8,7 @@
 
 #include <connectivity_plus/connectivity_plus_windows_plugin.h>
 #include <encrypter/encrypter_plugin_c_api.h>
+#include <firebase_core/firebase_core_plugin_c_api.h>
 #include <url_launcher_windows/url_launcher_windows.h>
 
 void RegisterPlugins(flutter::PluginRegistry* registry) {
@@ -15,6 +16,8 @@ void RegisterPlugins(flutter::PluginRegistry* registry) {
       registry->GetRegistrarForPlugin("ConnectivityPlusWindowsPlugin"));
   EncrypterPluginCApiRegisterWithRegistrar(
       registry->GetRegistrarForPlugin("EncrypterPluginCApi"));
+  FirebaseCorePluginCApiRegisterWithRegistrar(
+      registry->GetRegistrarForPlugin("FirebaseCorePluginCApi"));
   UrlLauncherWindowsRegisterWithRegistrar(
       registry->GetRegistrarForPlugin("UrlLauncherWindows"));
 }