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>

go.mod

@@ -1,6 +1,6 @@
 module music-server
 
-go 1.25.0
+go 1.26.0
 
 require (
 	github.com/MShekow/directory-checksum v1.4.18
@@ -11,7 +11,7 @@ require (
 	github.com/labstack/echo/v5 v5.3.0
 	github.com/lib/pq v1.12.3 // indirect
 	github.com/spf13/afero v1.15.0
-	github.com/stretchr/testify v1.11.1
+	github.com/stretchr/testify v1.12.1
 	github.com/testcontainers/testcontainers-go v0.42.0
 	go.uber.org/zap v1.28.0
 )
@@ -20,7 +20,9 @@ require (
 	github.com/danielgtaylor/huma/v2 v2.39.1
 	github.com/getkin/kin-openapi v0.149.0
 	github.com/google/uuid v1.6.0
-	golang.org/x/sync v0.22.0
+	github.com/prometheus/client_golang v1.25.0
+	github.com/prometheus/client_model v0.6.3
+	golang.org/x/sync v0.23.0
 )
 
 require (
@@ -29,6 +31,7 @@ require (
 	github.com/Microsoft/go-winio v0.6.2 // indirect
 	github.com/a-h/parse v0.0.0-20250122154542-74294addb73e // indirect
 	github.com/andybalholm/brotli v1.2.2 // indirect
+	github.com/beorn7/perks v1.0.1 // indirect
 	github.com/cenkalti/backoff/v4 v4.3.0 // indirect
 	github.com/cespare/xxhash/v2 v2.3.0 // indirect
 	github.com/cli/browser v1.3.0 // indirect
@@ -37,7 +40,6 @@ require (
 	github.com/containerd/log v0.1.0 // indirect
 	github.com/containerd/platforms v0.2.1 // indirect
 	github.com/cpuguy83/dockercfg v0.3.2 // indirect
-	github.com/davecgh/go-spew v1.1.2-0.20180830191138-d8f796af33cc // indirect
 	github.com/distribution/reference v0.6.0 // indirect
 	github.com/docker/go-units v0.5.0 // indirect
 	github.com/ebitengine/purego v0.10.0 // indirect
@@ -55,7 +57,8 @@ require (
 	github.com/jackc/pgpassfile v1.0.0 // indirect
 	github.com/jackc/pgservicefile v0.0.0-20240606120523-5a60cdf6a761 // indirect
 	github.com/jackc/puddle/v2 v2.2.2 // indirect
-	github.com/klauspost/compress v1.19.0 // indirect
+	github.com/klauspost/compress v1.20.1 // indirect
+	github.com/kylelemons/godebug v1.1.0 // indirect
 	github.com/labstack/echo/v4 v4.15.4 // indirect
 	github.com/labstack/gommon v0.5.0 // indirect
 	github.com/lufia/plan9stats v0.0.0-20211012122336-39d0f177ccd0 // indirect
@@ -71,13 +74,15 @@ require (
 	github.com/moby/sys/user v0.4.0 // indirect
 	github.com/moby/sys/userns v0.1.0 // indirect
 	github.com/moby/term v0.5.2 // indirect
+	github.com/munnerz/goautoneg v0.0.0-20191010083416-a7dc8b61c822 // indirect
 	github.com/natefinch/atomic v1.0.1 // indirect
 	github.com/oasdiff/yaml v0.1.1 // indirect
 	github.com/oasdiff/yaml3 v0.0.14 // indirect
 	github.com/opencontainers/go-digest v1.0.0 // indirect
 	github.com/opencontainers/image-spec v1.1.1 // indirect
-	github.com/pmezard/go-difflib v1.0.1-0.20181226105442-5d4384ee4fb2 // indirect
 	github.com/power-devops/perfstat v0.0.0-20240221224432-82ca36839d55 // indirect
+	github.com/prometheus/common v0.72.0 // indirect
+	github.com/prometheus/procfs v0.22.0 // indirect
 	github.com/santhosh-tekuri/jsonschema/v6 v6.0.3 // indirect
 	github.com/shirou/gopsutil/v4 v4.26.3 // indirect
 	github.com/sirupsen/logrus v1.9.4 // indirect
@@ -92,14 +97,15 @@ require (
 	go.opentelemetry.io/otel/metric v1.41.0 // indirect
 	go.opentelemetry.io/otel/trace v1.41.0 // indirect
 	go.uber.org/multierr v1.10.0 // indirect
-	golang.org/x/crypto v0.54.0 // indirect
-	golang.org/x/mod v0.37.0 // indirect
-	golang.org/x/net v0.57.0 // indirect
-	golang.org/x/sys v0.47.0 // indirect
-	golang.org/x/text v0.40.0 // indirect
+	go.yaml.in/yaml/v3 v3.0.5 // indirect
+	golang.org/x/crypto v0.57.0 // indirect
+	golang.org/x/mod v0.41.0 // indirect
+	golang.org/x/net v0.59.0 // indirect
+	golang.org/x/sys v0.48.0 // indirect
+	golang.org/x/text v0.42.0 // indirect
 	golang.org/x/time v0.15.0 // indirect
-	golang.org/x/tools v0.47.0 // indirect
-	gopkg.in/yaml.v3 v3.0.1 // indirect
+	golang.org/x/tools v0.49.0 // indirect
+	google.golang.org/protobuf v1.36.12 // indirect
 )
 
 tool github.com/a-h/templ/cmd/templ