feat: implement tool-session progress panel and live list updates

- Add SessionOperationsContext + SessionProgressPanel for global,
  non-blocking lifecycle progress (create/start/stop/restart/delete/
  recreate-tunnel) driven by SSE events.
- Promote SessionsContext to authoritative shared session state with
  refresh, addOrUpdateSession, and removeSession helpers.
- Wire AppShell, DashboardPage, SessionsPage, useInstanceActions,
  ToolStarter, and InstanceList into shared state so lists update
  immediately after create/delete without manual refresh.
- Remove legacy blocking overlays from CreateSessionForm, SessionCard,
  and InstanceList; keep disabled states and inline spinners only.
- Update DashboardPage tests to wrap with SessionsProvider and
  SessionOperationsProvider.
- Add .cache/ to .gitignore.

Quality gates: npm run typecheck, npm run lint, npm test -- --run
(82 passed).

apps/web/src/components/features/tool/instance-list.tsx

@@ -17,6 +17,7 @@ import {
 } from "../../../api/config-profiles";
 import { listSSHKeys, type SSHKey } from "../../../api/ssh-keys";
 import { useEventContext } from "../../../state/events";
+import { useSessions } from "../../../state/sessions";
 
 const API_BASE_URL =
 	import.meta.env.VITE_API_BASE_URL ?? "http://localhost:8000";
@@ -37,6 +38,7 @@ export const InstanceList = ({
 	toolTypes,
 }: InstanceListProps) => {
 	const navigate = useNavigate();
+	const { refreshSessions } = useSessions();
 	const [instances, setInstances] = useState<ToolInstance[]>([]);
 	const [loading, setLoading] = useState(false);
 	const [showCreate, setShowCreate] = useState(false);
@@ -108,6 +110,7 @@ export const InstanceList = ({
 	const handleCreateSuccess = async () => {
 		setShowCreate(false);
 		await loadInstances();
+		await refreshSessions();
 	};
 
 	const loadConfigProfiles = useCallback(
@@ -196,6 +199,7 @@ export const InstanceList = ({
 			await deleteInstance(projectId, repoId, instanceId);
 			// Update state immediately instead of reloading
 			setInstances((prev) => prev.filter((i) => i.id !== instanceId));
+			await refreshSessions();
 		} catch {
 			setError("Failed to delete instance");
 		} finally {
@@ -245,15 +249,7 @@ export const InstanceList = ({
 			) : (
 				<div className="instance-grid">
 					{instances.map((instance) => (
-						<div
-							key={instance.id}
-							className={`instance-card ${busyInstanceId === instance.id ? "busy" : ""}`}
-						>
-							{busyInstanceId === instance.id && (
-								<div className="instance-busy-overlay">
-									<Icon name="loading" size="md" />
-								</div>
-							)}
+						<div key={instance.id} className="instance-card">
 							<div className="instance-info">
 								<div className="instance-name">{instance.display_name}</div>
 								<div className="instance-meta">