fix(extension): delete the dead chat-queue client surface

The sidebar-command handler in background.js POSTed to a server endpoint that
no longer exists (deleted with the chat queue) — ~35 lines of fully-wired dead
code including error handling for the permanent 404, plus its allowlist entry.
No sender in the extension ever emitted the message type.

chatEnabled leaves the /health contract (server hardcoded false, background.js
re-derived it, nothing consumed it — the chat input element it guarded is gone
from sidepanel.html). BROWSE_SIDEBAR_CHAT env flag had zero readers.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

browse/test/sidebar-tabs.test.ts

@@ -205,8 +205,9 @@ describe('server.ts: chat / sidebar-agent endpoints are gone', () => {
     expect(slice).not.toContain('agentStatus');
     expect(slice).not.toContain('messageQueue');
     expect(slice).not.toContain('agentStartTime');
-    // chatEnabled is hardcoded false now (older clients still see the field).
-    expect(slice).toMatch(/chatEnabled:\s*false/);
+    // chatEnabled is gone entirely — the chat pane no longer exists in any
+    // extension build, so /health stopped advertising a chat mode.
+    expect(slice).not.toContain('chatEnabled');
     // terminalPort survives.
     expect(slice).toContain('terminalPort');
   });