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