tim plugin, chat bot sync notifications, test fixes

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

public/plugins/tim/plugin.json

@@ -0,0 +1,10 @@
+{
+    "name": "tim",
+    "version": "1.0.0",
+    "description": "Time calculator — duration between two times, add duration to time, end-of-day for target work hours.",
+    "frontend": {
+        "js": ["tim.js"],
+        "css": ["tim.css"],
+        "html": ["tim.html"]
+    }
+}