feat(ui): gate the pull-request surface on GitHub, move the account into it, and GitHub sign-in into Integrations

The pull-request rail icon now appears only while GitHub is connected
(OAuth or gh CLI), like Linear; Linear sits after the walkthrough in the
default rail order. The GitHub account avatar and switcher leave the
header for the pull-request panel, where the walkthrough, refresh, and
account controls share one row and one height, and the account stays
visible on the panel's empty state. A manual refresh keeps its spinner on
screen long enough to read as work done.

GitHub sign-in moves from Settings → Git to Settings → Integrations →
Built-in integrations as a card before Linear; search and the connect
buttons follow it.

packages/ui/src/components/sections/openchamber/OpenChamberPage.tsx

@@ -7,7 +7,6 @@ import { AppLinkSecuritySettings } from './AppLinkSecuritySettings';
 import { DefaultsSettings } from './DefaultsSettings';
 import { GitSettings } from './GitSettings';
 import { NotificationSettings } from './NotificationSettings';
-import { GitHubSettings } from './GitHubSettings';
 import { VoiceSettings } from './VoiceSettings';
 import { TunnelSettings } from './TunnelSettings';
 import { OpenCodeCliSettings } from './OpenCodeCliSettings';
@@ -78,8 +77,6 @@ export const OpenChamberPage: React.FC<OpenChamberPageProps> = ({ section }) =>
                 return <ShortcutsSectionContent />;
             case 'git':
                 return <GitSectionContent />;
-            case 'github':
-                return <GitHubSectionContent />;
             case 'notifications':
                 return <NotificationSectionContent />;
             case 'voice':
@@ -233,14 +230,6 @@ const GitSectionContent: React.FC = () => {
     return <GitSettings />;
 };
 
-// GitHub section: Connect account for PR/issue workflows
-const GitHubSectionContent: React.FC = () => {
-    if (isVSCodeRuntime()) {
-        return null;
-    }
-    return <GitHubSettings />;
-};
-
 // Notifications section: Native browser notifications
 const NotificationSectionContent: React.FC = () => {
     return <NotificationSettings />;