feat: redirect root path based on auth state

/ now checks for an authenticated session:
- Authenticated users → 303 redirect to /sources
- Unauthenticated users → 303 redirect to /pages/login

Removes the old index page template rendering and formatUptime
helper (now dead code). Adds tests for both redirect cases.

README.md

@@ -652,7 +652,7 @@ against a misbehaving sender).
 
 | Method | Path                        | Description |
 | ------ | --------------------------- | ----------- |
-| `GET`  | `/`                         | Web UI index page (server-rendered) |
+| `GET`  | `/`                         | Root redirect (authenticated → `/sources`, unauthenticated → `/pages/login`) |
 | `GET`  | `/.well-known/healthcheck`  | Health check (JSON: status, uptime, version) |
 | `GET`  | `/s/*`                      | Static file serving (embedded CSS, JS) |
 | `ANY`  | `/webhook/{uuid}`           | Webhook receiver endpoint (accepts all methods) |