Expose Prometheus metrics on a separate port

Metrics are served on METRICS_PORT (default 2112, "off" to disable), never on
the public port. Besides the Go runtime and process metrics this adds:

- http_requests_total and http_request_duration_seconds per route pattern,
  from an Echo middleware.
- musicserver_songs_requested_total and musicserver_songs_played_total by
  pick mode (random, low, classic). The mode is now stored with each queued
  song (migration 000006, not released yet).
- Library size, sync duration, last successful sync, broken songs from the
  last full sync, and the database connection pool.

Refs #35, #36, #37

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

internal/metrics/pool_test.go

@@ -0,0 +1,33 @@
+package metrics
+
+import (
+	"context"
+	"strings"
+	"testing"
+
+	"github.com/jackc/pgx/v5/pgxpool"
+	"github.com/prometheus/client_golang/prometheus"
+	"github.com/prometheus/client_golang/prometheus/testutil"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestPoolCollector(t *testing.T) {
+	// The pool connects lazily, so no database is needed to read its statistics.
+	pool, err := pgxpool.New(context.Background(), "postgres://user:pass@127.0.0.1:1/music?pool_max_conns=7")
+	require.NoError(t, err)
+	t.Cleanup(pool.Close)
+
+	registry := prometheus.NewRegistry()
+	registry.MustRegister(NewPoolCollector(pool))
+
+	assert.Equal(t, 11, testutil.CollectAndCount(registry))
+	require.NoError(t, testutil.GatherAndCompare(registry, strings.NewReader(`
+# HELP musicserver_db_pool_max_conns Most connections the pool opens.
+# TYPE musicserver_db_pool_max_conns gauge
+musicserver_db_pool_max_conns 7
+# HELP musicserver_db_pool_acquired_conns Connections in use.
+# TYPE musicserver_db_pool_acquired_conns gauge
+musicserver_db_pool_acquired_conns 0
+`), "musicserver_db_pool_max_conns", "musicserver_db_pool_acquired_conns"))
+}