feat: wire main loop with periodic sync+scan and sync_interval config

Replace compute-only run() with an immediate sync+scan followed by a
ticker-driven periodic loop, add the sync.interval config field (default
6h) with defaults and validation, and add tests for the scheduling logic.

docs/plans/2026-07-19-notifier-webui-sync.md

@@ -101,10 +101,10 @@ name collisions.)
 - [x] run tests - must pass before task 4
 
 ### Task 4: Main loop wiring (sync → scan)
-- [ ] replace compute-only `run()` with: one immediate sync+scan, then a ticker-driven periodic sync+scan goroutine; keep graceful shutdown via ctx
-- [ ] add a `syncInterval` config field (default e.g. 6h) to `config.go` + defaults + validation
-- [ ] write tests for the loop scheduling logic where feasible (ticker fires, ctx cancels cleanly)
-- [ ] run tests - must pass before task 5
+- [x] replace compute-only `run()` with: one immediate sync+scan, then a ticker-driven periodic sync+scan goroutine; keep graceful shutdown via ctx
+- [x] add a `syncInterval` config field (default e.g. 6h) to `config.go` + defaults + validation
+- [x] write tests for the loop scheduling logic where feasible (ticker fires, ctx cancels cleanly)
+- [x] run tests - must pass before task 5
 
 ### Task 5: Notifier — Telegram sender + digest
 - [ ] define `Sender` interface (`Send(ctx, message string) error`) and a `telegramSender` using `TelegramConfig` (bot API `sendMessage`)