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/src/cli.ts

@@ -1085,7 +1085,6 @@ Refs:           After 'snapshot', use @e1, @e2... as selectors:
       const serverEnv: Record<string, string> = {
         BROWSE_HEADED: '1',
         BROWSE_PORT: '34567',
-        BROWSE_SIDEBAR_CHAT: '1',
         // Disable parent-process watchdog: the user controls the headed browser
         // window lifecycle. The CLI exits immediately after connect, so watching
         // it would kill the server ~15s later. Cleanup happens via browser

browse/src/server.ts

@@ -1832,10 +1832,6 @@ export function buildFetchHandler(cfg: ServerConfig): ServerHandle {
           mode: browserManager.getConnectionMode(),
           uptime: Math.floor((Date.now() - startTime) / 1000),
           tabs: browserManager.getTabCount(),
-          // The chat queue is gone — Terminal pane is the sole sidebar
-          // surface. Keep `chatEnabled: false` so any older extension
-          // build still treats the chat input as disabled.
-          chatEnabled: false,
           // Security module status — drives the shield icon in the sidepanel.
           // Returns {status: 'protected'|'degraded'|'inactive', layers: {...}}.
           // The chat-path classifier no longer feeds this since