perf(tooling): add automated streaming profiler

Adds `bun run profile:session`: creates a session, opens it in a real
browser, dispatches a prompt through the supported `openchamber session` CLI,
and records until the session reports itself idle. No input is synthesised, so
everything captured is the app reacting to its own event stream.

Streaming is judged by responsiveness rather than totals, so the report leads
with the long-task distribution, style recalculation and layout rates, frame
production, and the application's own stream counters.

Two failure modes are detected rather than reported as clean results. A session
belonging to a directory the browser is not viewing renders nothing and
produces a perfectly quiet profile, so the run verifies both new message
elements in the DOM and message-list render counters. And `RunTask` is only
emitted under the disabled-by-default timeline category, so a capture without
it reports zero long tasks; the missing-task case is now called out instead of
being shown as zero.

Metric helpers are shared with the idle profiler.

package.json

@@ -82,7 +82,8 @@
     "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",
-    "profile:idle": "node scripts/profile-idle.mjs"
+    "profile:idle": "node scripts/profile-idle.mjs",
+    "profile:session": "node scripts/profile-session.mjs"
   },
   "dependencies": {
     "@base-ui/react": "^1.4.0",