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.

internal/handlers/handlers.go

@@ -65,7 +65,6 @@ func New(lc fx.Lifecycle, params HandlersParams) (*Handlers, error) {
 
 	// Parse all page templates once at startup
 	s.templates = map[string]*template.Template{
-		"index.html":         parsePageTemplate("index.html"),
 		"login.html":         parsePageTemplate("login.html"),
 		"profile.html":       parsePageTemplate("profile.html"),
 		"sources_list.html":  parsePageTemplate("sources_list.html"),