perf(tooling): add automated idle profiling harness

Adds `bun run profile:idle`: a fully unattended capture of what OpenChamber
does while nobody interacts with it. It reports main-thread busy time, style
recalculation and layout rates, DOM node and listener growth, heap trajectory,
a CPU sampling profile, and per-call-site attribution of timer, animation
frame, and observer work.

Chrome throttles timers and stops producing frames for occluded or backgrounded
windows, which silently reports an idle-looking renderer regardless of what the
page schedules. Launch flags now disable that throttling, and every run measures
frame liveness so a throttled capture is reported as a warning rather than as a
clean result.

CDP launch and client code is shared with the existing browser profiler.

package.json

@@ -81,7 +81,8 @@
     "release:prepare": "bun run build && bun run type-check && bun run lint",
     "release:test": "./scripts/test-release-build.sh",
     "release:test:intel": "./scripts/test-release-build.sh x86_64",
-    "release:test:arm": "./scripts/test-release-build.sh aarch64"
+    "release:test:arm": "./scripts/test-release-build.sh aarch64",
+    "profile:idle": "node scripts/profile-idle.mjs"
   },
   "dependencies": {
     "@base-ui/react": "^1.4.0",