feat: Minstrel backs itself up nightly to a folder or an S3 bucket, off until an admin switches it on (#6773)

Admin › Backups shows a verdict first (off, not set up, waiting, backed up,
overdue, failing since when), Back up now, Test destination and the latest
runs, with the settings beside them.

- backup.Service: one run at a time, bounded at 30 minutes; the schedule
  ticks every 5 minutes, catches up a slot missed while the server was down,
  and retries a failure after an hour and then after as long as it has been
  failing. Runs are recorded in backup_runs, pruned after 90 days; a run cut
  off by a shutdown is marked failed at the next start.
- A folder destination writes database/minstrel-<UTC stamp>.tar and refuses
  a folder that isn't there. An S3 destination stages the file, hashes it,
  and uploads it under database/ through a throttled reader (4 MiB/s by
  default, 0 for no limit).
- Test destination checks the form as typed and only lists.
- The bucket secret is sealed like every stored credential; backup_settings
  and backup_runs are left out of the backup itself.
- The panel polls only while a run is going, capped at the run limit plus
  five minutes.

The music switch named in the task is left to #6774, so no control ships
that does nothing.

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

cmd/minstrel/main.go

@@ -16,6 +16,8 @@ import (
 	"github.com/jackc/pgx/v5/pgxpool"
 
 	"git.fabledsword.com/bvandeusen/minstrel/internal/acoustid"
+	"git.fabledsword.com/bvandeusen/minstrel/internal/backup"
+	"git.fabledsword.com/bvandeusen/minstrel/internal/buildinfo"
 	"git.fabledsword.com/bvandeusen/minstrel/internal/catalogue"
 	"git.fabledsword.com/bvandeusen/minstrel/internal/config"
 	"git.fabledsword.com/bvandeusen/minstrel/internal/coplay"
@@ -470,6 +472,11 @@ func run() error {
 	// The sweeper above holds this same instance, so a save from the admin
 	// card changes what it does on its next tick.
 	srv.ReacqSettings = reacqSettings
+	// The server's own backup: the loop runs the nightly schedule, and the
+	// admin page starts, tests and configures the same instance.
+	backups := backup.NewService(pool, logger.With("component", "backup"), buildinfo.Version)
+	go backups.Loop(ctx)
+	srv.Backups = backups
 	srv.StreamSecret = cfg.StreamSecret
 	httpServer := &http.Server{
 		Addr:              cfg.Server.Address,
@@ -510,6 +517,8 @@ func run() error {
 	if err := httpServer.Shutdown(shutdownCtx); err != nil {
 		return fmt.Errorf("shutdown: %w", err)
 	}
+	// A backup still running is stopped and records that it was cut off.
+	backups.Close()
 	logger.Info("minstrel stopped")
 	return nil
 }