feat(web): wire up MCP task support — Tasks screen, Run-as-task, status toasts (#1422) (#1424)

Wires the ported Tasks screen + core task subsystem through App.tsx: sticky Clear Completed, cancel/refresh error toasts, core-side per-task progress correlation, Run-as-task on the Tools screen (gated on server support), per-server Task TTL, and live task-status toasts.

clients/web/src/components/groups/ToolDetailPanel/ToolDetailPanel.stories.tsx

@@ -10,8 +10,11 @@ const meta: Meta<typeof ToolDetailPanel> = {
     onFormChange: fn(),
     onExecute: fn(),
     onCancel: fn(),
+    onRunAsTaskChange: fn(),
     formValues: {},
     isExecuting: false,
+    serverSupportsTaskToolCalls: false,
+    runAsTask: false,
   },
 };
 
@@ -142,3 +145,45 @@ export const WithProgress: Story = {
     formValues: { batchSize: 100 },
   },
 };
+
+const optionalTaskTool: Tool = {
+  name: "summarize_corpus",
+  description: "Summarizes a large corpus — can run as a background task",
+  execution: { taskSupport: "optional" },
+  inputSchema: {
+    type: "object",
+    properties: {
+      corpus: { type: "string", description: "Text to summarize" },
+    },
+  },
+};
+
+const requiredTaskTool: Tool = {
+  name: "train_model",
+  description: "Long-running training job — always runs as a task",
+  execution: { taskSupport: "required" },
+  inputSchema: {
+    type: "object",
+    properties: {
+      dataset: { type: "string", description: "Dataset id" },
+    },
+  },
+};
+
+// Server supports task tool calls + tool is `optional`: the toggle renders
+// enabled and off by default.
+export const RunAsTaskOptional: Story = {
+  args: {
+    tool: optionalTaskTool,
+    serverSupportsTaskToolCalls: true,
+    runAsTask: false,
+  },
+};
+
+// Tool is `required`: the toggle is forced on and disabled.
+export const RunAsTaskRequired: Story = {
+  args: {
+    tool: requiredTaskTool,
+    serverSupportsTaskToolCalls: true,
+  },
+};