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/ServerSettingsModal/ServerSettingsModal.stories.tsx

@@ -16,6 +16,7 @@ const initialSettings: InspectorServerSettings = {
   metadata: [{ key: "userId", value: "user-789" }],
   connectionTimeout: 30000,
   requestTimeout: 60000,
+  taskTtl: 60000,
   oauthClientId: "my-client-id",
   oauthClientSecret: "super-secret-value",
   oauthScopes: "read write",
@@ -67,6 +68,7 @@ export const EmptySettings: Story = {
       metadata: [],
       connectionTimeout: 30000,
       requestTimeout: 60000,
+      taskTtl: 60000,
     },
   },
 };

clients/web/src/components/groups/ServerSettingsModal/ServerSettingsModal.test.tsx

@@ -9,6 +9,7 @@ const initialSettings: InspectorServerSettings = {
   metadata: [{ key: "userId", value: "u-1" }],
   connectionTimeout: 30000,
   requestTimeout: 60000,
+  taskTtl: 60000,
   oauthClientId: "cid",
   oauthClientSecret: "secret",
   oauthScopes: "read",
@@ -19,6 +20,7 @@ const emptySettings: InspectorServerSettings = {
   metadata: [],
   connectionTimeout: 30000,
   requestTimeout: 60000,
+  taskTtl: 60000,
 };
 
 describe("ServerSettingsModal", () => {

clients/web/src/components/groups/ServerSettingsModal/ServerSettingsModal.tsx

@@ -83,7 +83,7 @@ export function ServerSettingsModal({
   }
 
   function handleTimeoutChange(
-    field: "connectionTimeout" | "requestTimeout",
+    field: "connectionTimeout" | "requestTimeout" | "taskTtl",
     value: number,
   ) {
     onSettingsChange({ ...settings, [field]: value });