diag: add startup-timing trace and /api/diag/timing endpoint

bbctrl.Trace records monotonic-anchored events from process start.
Ctrl, Comm, the Web layer and __init__ are instrumented so a single
GET /api/diag/timing returns a full timeline of import, controller
init, AVR connection, first websocket, and first GET /. The
restart-timing.js client posts performance.now() marks back so the
browser side can be aligned in the same view.

Used to drive the cold-boot optimisations that reduce listen latency
on the Pi by ~8s.

src/py/bbctrl/Web.py

@@ -798,6 +798,32 @@ class RemoteDiagnosticsHandler(bbctrl.APIHandler):
                     'message': e.reason or "Unknown"
                 })
 
+
+class TimingHandler(bbctrl.APIHandler):
+    """Return the bbctrl process startup timeline as JSON.
+
+    Includes monotonic-anchored events from bbctrl.Trace, the wall
+    clock anchor (so the timeline can be aligned with journalctl /
+    systemd-analyze output), and the most recent UI-side timing
+    payload posted by the browser.
+    """
+    def get(self):
+        import bbctrl.Trace as _T
+        self.write_json(_T.timeline())
+
+
+class UITimingHandler(bbctrl.APIHandler):
+    """Browser posts its performance.now() marks here once per load."""
+    def put_ok(self):
+        import bbctrl.Trace as _T
+        # self.json is parsed in APIHandler.prepare()
+        try:
+            _T.set_ui_timing(self.json)
+            _T.mark('ui.posted_timing',
+                    marks=len(self.json.get('marks', []) or []))
+        except Exception: pass
+
+
 # Base class for Web Socket connections
 class ClientConnection(object):
     def __init__(self, app):
@@ -873,6 +899,12 @@ class SockJSConnection(ClientConnection, sockjs.tornado.SockJSConnection):
             ip = info.ip
             if 'X-Real-IP' in info.headers: ip = info.headers['X-Real-IP']
             self.app.get_ctrl(id).log.get('Web').info('Connection from %s' % ip)
+            try:
+                if not getattr(self.app, '_first_ws', False):
+                    self.app._first_ws = True
+                    import bbctrl.Trace as _T
+                    _T.mark('ws.first_open', ip=ip)
+            except Exception: pass
             super().on_open(id)
 
 
@@ -881,6 +913,23 @@ class StaticFileHandler(tornado.web.StaticFileHandler):
         self.set_header('Cache-Control',
                         'no-store, no-cache, must-revalidate, max-age=0')
 
+    def prepare(self):
+        # Mark the first request for the index page so we can see when
+        # chromium actually started fetching the UI on cold boot.
+        try:
+            app = self.application
+            if not getattr(app, '_first_root_get', False):
+                # Treat any GET '/' or '/index.html' as the root fetch.
+                p = self.request.path
+                if p in ('/', '/index.html', ''):
+                    app._first_root_get = True
+                    import bbctrl.Trace as _T
+                    _T.mark('web.first_root_get',
+                            ip=self.request.remote_ip,
+                            ua=(self.request.headers.get('User-Agent') or '')[:60])
+        except Exception: pass
+        return super().prepare()
+
 class Web(tornado.web.Application):
     def __init__(self, args, ioloop):
         self.args = args
@@ -902,6 +951,8 @@ class Web(tornado.web.Application):
 
         handlers = [
             (r'/websocket', WSConnection),
+            (r'/api/diag/timing', TimingHandler),
+            (r'/api/diag/timing/ui', UITimingHandler),
             (r'/api/log', LogHandler),
             (r'/api/message/(\d+)/ack', MessageAckHandler),
             (r'/api/bugreport', BugReportHandler),