v1.12.1: rich status indicator + server-side workspace pane sync

Status indicator (StatusDot): drops the flat amber pulse for a richer set
of states — orbiting amber for streaming, spinning sky ring for tool_running,
static violet for waiting_for_input, plus the existing idle/error. Backend
chat_status frame widens from 'working|idle|error' to discriminate streaming
vs tool execution vs paused for user input.

Workspace pane sync: pane layout moves from per-device localStorage to
server-side sessions.workspace_panes jsonb. PATCH /api/sessions/:id/workspace
broadcasts session_workspace_updated on the user channel for cross-device live
sync. Echo dedup via JSON comparison so the round-trip frame doesn't loop.
Legacy localStorage seeds the server on first hydrate, then is deleted.
Deprecated session_panes table dropped.

Resilience: startup sweep marks any stale 'streaming' message older than
5 minutes as 'failed' so v1.12.0-style hung rows clear on container restart.
useWorkspacePanes gains validatePanes() to prune dead chatId references from
saved pane state when the chat list lands.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/web/src/api/client.ts

@@ -143,6 +143,11 @@ export const api = {
       ),
     openChatsCount: (id: string) =>
       request<{ count: number }>(`/api/sessions/${id}/chats/open-count`),
+    updateWorkspacePanes: (id: string, panes: Session['workspace_panes']) =>
+      request<Session>(`/api/sessions/${id}/workspace`, {
+        method: 'PATCH',
+        body: JSON.stringify({ workspace_panes: panes }),
+      }),
   },
 
   chats: {