tests: UI + API smoke tests for chat plugin

Covers the flyout lifecycle (footer button, toggle, header-back
visibility tracking thread/list view), the pick-view detour, DOM
structural invariants (peer strip inside thread view, form/input/send
present) and the three read-only chat endpoints. Send/receive requires
a real relay and is intentionally skipped.

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

public/plugins/tests/tests.js

@@ -54,6 +54,7 @@ const FILES = [
     './asset-picker.test.js',
     './terminal.test.js',
     './theme.test.js',
+    './chat.test.js',
 ];
 
 // Await all imports so the runner can start in a deterministic state.