fix: clean up tab titles and sidebar session display

- Remove useless document.title from handleOpen (it only changed the
  caller page's title, not the new tab)
- Terminal tab title: simpler format without extra '— Headquarter' suffix
  - Single session: '{name} — Terminal'
  - Multiple sessions: '{name} · {session_name} — Terminal'
- Sidebar live sessions: show tool type in small muted text next to
  display_name so sessions aren't indistinguishable when display_name
  is just the workspace name

Quality gates: tsc --noEmit pass, npm run build pass, 82/82 tests pass

apps/web/src/components/app-shell.tsx

@@ -63,7 +63,10 @@ const SessionItem = ({ session }: { session: Session }) => {
 		>
 			<span className={`session-status ${isRunning ? "running" : ""}`} />
 			<Icon name={session.tool_icon as IconName} size="sm" />
-			<span className="session-name">{session.display_name}</span>
+			<span className="session-name">
+				{session.display_name}
+				<span className="session-tool">{session.tool_type_name}</span>
+			</span>
 		</a>
 	);
 };