analytics: distinct power_trial_started event (vs generic trial_started)

PostHog couldn't tell a Power-trial signup from a Pro/managed-trial signup —
both fired trial_started. Now every path that starts a Power trial (sign-in
auto-enroll, the Settings button, the daemon self-heal net) fires
power_trial_started with a method property (signin | button | daemon_net), so
Power vs Pro trial funnels are separable.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_019GTBZjBGurqsHUHsjaU1gA

Author: sodiumsun

heard/daemon.py

@@ -1265,6 +1265,12 @@ def _maybe_autostart_power_trial(self, me: dict) -> None:
                     config.set_value("heard_trial_expires_at", exp)
                 config.set_value("power_trial_used", True)
                 _log("power_trial_autostarted", via="daemon_poll")
+                try:
+                    from heard import analytics
+
+                    analytics.capture("power_trial_started", {"method": "daemon_net"})
+                except Exception:
+                    pass
                 self._reload_config()
             else:
                 _log("power_trial_autostart_noop", reason=str(data.get("reason") or "not_power"))

heard/home_window.py

@@ -830,6 +830,12 @@ def _work():
                         exp = int(data.get("trial_expires_at") or 0)
                         if exp:
                             config.set_value("heard_trial_expires_at", exp)
+                        try:
+                            from heard import analytics
+
+                            analytics.capture("power_trial_started", {"method": "button"})
+                        except Exception:
+                            pass
                         _reload_daemon()
                     else:
                         # trial_used / ineligible — tell the user, stay put.

heard/url_scheme.py

@@ -105,6 +105,12 @@ def _maybe_start_power_trial(token: str) -> None:
             if exp:
                 config.set_value("heard_trial_expires_at", exp)
             print(f"[power_trial] sign-in autostart OK (exp={exp})")
+            try:
+                from heard import analytics
+
+                analytics.capture("power_trial_started", {"method": "signin"})
+            except Exception:
+                pass
         else:
             # Not power — usually a brand-new-account race (account not queryable
             # yet). The daemon's /v1/me poll retries this within ~5 min, so it