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/db/migrations/000006_add_fingerprint_and_queue.up.sql

@@ -7,8 +7,9 @@ ALTER TABLE soundtrack ADD COLUMN fingerprint TEXT NOT NULL DEFAULT '';
 CREATE TABLE queue (
     uuid UUID PRIMARY KEY DEFAULT gen_random_uuid(),
     current_song INT4 NOT NULL DEFAULT -1,
-    -- The last random song, added to the queue by /music/addQue.
+    -- The last random song, added to the queue by /music/addQue, and how it was picked.
     last_fetched_song_uuid UUID NULL,
+    last_fetched_mode VARCHAR(10) NULL,
     started_at TIMESTAMPTZ NOT NULL DEFAULT NOW(),
     ended_at TIMESTAMPTZ NULL
 );
@@ -21,6 +22,8 @@ CREATE TABLE queue_song (
     song_uuid UUID NOT NULL,
     soundtrack_name VARCHAR NOT NULL,
     song_name VARCHAR NOT NULL,
+    -- How the song was picked: random, low or classic.
+    mode VARCHAR(10) NOT NULL,
     added_at TIMESTAMPTZ NOT NULL DEFAULT NOW(),
     PRIMARY KEY (queue_uuid, song_no)
 );