feat(backup): daily server and user backups, restore by section (backend)

Admins switch automatic backups on, pick the time and the retention
(default 03:00, 3 days). Each run writes a gzip snapshot of the whole
database (VACUUM INTO, consistent while others write) and one MindSift
backup ZIP per active user below $DATA_DIR/backups, then deletes files
past the retention. A restart after the time catches up on that day.
Admins list, download and trigger runs; users list, download and restore
their own backups.

Import and restore can be limited to sections (notes, tasks, lists,
inbox, themes): restore only empties the chosen sections. Export and
import now carry custom themes. File names are checked against a fixed
pattern, so no other file can be fetched through the API.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

internal/api/server.go

@@ -56,6 +56,9 @@ func NewServer(cfg *config.Config, store *storage.Store, wsHub *ws.Hub, staticFS
 	if cfg.DemoMode && cfg.DemoResetMinutes > 0 {
 		go srv.startDemoResetTicker()
 	}
+	if !cfg.DemoMode {
+		go srv.startBackupScheduler()
+	}
 	return srv
 }
 
@@ -130,6 +133,9 @@ func (s *Server) Router() http.Handler {
 		r.Get("/api/v1/stats", s.handleStats)
 		r.Get("/api/v1/search", s.handleSearch)
 		r.Get("/api/v1/export", s.handleExport)
+		r.Get("/api/v1/backups", s.handleListMyBackups)
+		r.Get("/api/v1/backups/{name}", s.handleDownloadMyBackup)
+		r.Post("/api/v1/backups/{name}/restore", s.handleRestoreMyBackup)
 		r.Get("/api/v1/export/markdown", s.handleExportMarkdown)
 		r.Post("/api/v1/import/mindsift", s.handleImportMindSift)
 		r.Delete("/api/v1/user/data", s.handlePurgeOwnData)
@@ -256,6 +262,9 @@ func (s *Server) Router() http.Handler {
 		r.Group(func(r chi.Router) {
 			r.Use(s.adminMiddleware)
 			r.Get("/api/v1/admin/settings", s.handleAdminGetSettings)
+			r.Get("/api/v1/admin/backups", s.handleAdminListBackups)
+			r.Post("/api/v1/admin/backups", s.handleAdminRunBackup)
+			r.Get("/api/v1/admin/backups/{name}", s.handleAdminDownloadBackup)
 			r.Put("/api/v1/admin/settings", s.handleAdminUpdateSettings)
 			r.Get("/api/v1/admin/settings/sharing-impact", s.handleAdminSharingImpact)