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/database/database.go

@@ -13,6 +13,7 @@ import (
 	_ "modernc.org/sqlite" // Register sqlite driver.
 
 	"yellowjacket/backend/database/sql/sqlcgen"
+	"yellowjacket/backend/profiling"
 	"yellowjacket/backend/system"
 )
 
@@ -31,6 +32,8 @@ type DB struct {
 
 // NewDB opens the database and applies schema migrations.
 func NewDB(logger *slog.Logger) (*DB, error) {
+	defer profiling.TimeOp(logger, "database.NewDB")()
+
 	dbCtx := context.Background()
 
 	userDataDir, err := system.GetUserDataDirPath()