add dev-only profiling with pprof, runtime/trace, and operation timing

Wire up Go's standard profiling toolkit so it's automatically available
in dev builds and completely absent from production. The profiling
package uses build tags (dev/!dev) to eliminate all pprof, trace, and
timing code from release binaries with zero new dependencies.

- backend/profiling: pprof HTTP server on :6060, /debug/trace endpoint,
  block/mutex profiling, and TimeOp helper for structured operation timing
- scripts/profile.sh: interactive menu-driven script that auto-selects
  free ports (8080-8089) so multiple profiles can be open simultaneously
- Instrumented key operations: app init, database init, player load/restore,
  queue set/restore
- Makefile targets: profile, profile-cpu, profile-heap, profile-trace
- .gitignore: exclude trace-*.out and *.pprof artifacts

backend/profiling/doc.go

@@ -0,0 +1,56 @@
+// Package profiling provides dev-only performance profiling via pprof and runtime/trace.
+//
+// In dev builds (build tag "dev"), Start launches an HTTP server on localhost:6060
+// exposing the standard pprof endpoints and a /debug/trace endpoint for capturing
+// execution traces. It also enables block and mutex profiling at reasonable sampling
+// rates.
+//
+// In production builds, all exported functions are no-ops and the pprof/trace
+// imports are excluded from the binary entirely.
+//
+// # Quick start
+//
+// Run the app in dev mode (pprof starts automatically):
+//
+//	make dev
+//
+// Then, in a separate terminal, use the interactive profiling helper:
+//
+//	./scripts/profile.sh
+//
+// The script provides a menu-driven interface that opens results in your
+// browser as flame graphs. No pprof knowledge required. You can also
+// invoke it directly:
+//
+//	./scripts/profile.sh cpu       # CPU profile
+//	./scripts/profile.sh heap      # Heap (memory) profile
+//	./scripts/profile.sh allocs    # Allocation profile
+//	./scripts/profile.sh goroutine # Goroutine dump
+//	./scripts/profile.sh block     # Block (sync) profile
+//	./scripts/profile.sh mutex     # Mutex contention profile
+//	./scripts/profile.sh trace     # Execution trace
+//	./scripts/profile.sh health    # Quick runtime health check
+//
+// # Manual usage
+//
+// If you prefer the CLI directly:
+//
+//	go tool pprof http://localhost:6060/debug/pprof/profile?seconds=30   # CPU
+//	go tool pprof http://localhost:6060/debug/pprof/heap                 # Memory
+//	go tool pprof http://localhost:6060/debug/pprof/goroutine            # Goroutines
+//	curl -o trace.out http://localhost:6060/debug/trace?seconds=5        # Trace
+//	go tool trace trace.out
+//
+// # Programmatic usage
+//
+//	stop := profiling.Start(logger)
+//	defer stop()
+//
+// # Operation timing
+//
+// Use TimeOp to log the duration of any operation in dev builds:
+//
+//	defer profiling.TimeOp(logger, "player.LoadFile")()
+//
+// In production builds TimeOp is a no-op with zero overhead.
+package profiling