feat(workspace): add context field for AI agent background info

Add a `context` text field to workspaces, allowing users to provide
background information and context for AI agents working in the
workspace. Full stack: migration, sqlc queries, Go handler, TS types,
SDK, and settings page UI.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/web/app/(dashboard)/settings/page.tsx

@@ -95,6 +95,7 @@ export default function SettingsPage() {
   const [description, setDescription] = useState(
     workspace?.description ?? "",
   );
+  const [context, setContext] = useState(workspace?.context ?? "");
   const [profileName, setProfileName] = useState(user?.name ?? "");
   const [avatarUrl, setAvatarUrl] = useState(user?.avatar_url ?? "");
   const [saving, setSaving] = useState(false);
@@ -115,6 +116,7 @@ export default function SettingsPage() {
   useEffect(() => {
     setName(workspace?.name ?? "");
     setDescription(workspace?.description ?? "");
+    setContext(workspace?.context ?? "");
   }, [workspace]);
 
   useEffect(() => {
@@ -130,6 +132,7 @@ export default function SettingsPage() {
       const updated = await api.updateWorkspace(workspace.id, {
         name,
         description: description || undefined,
+        context: context || undefined,
       });
       updateWorkspace(updated);
       setSaved(true);
@@ -330,6 +333,19 @@ export default function SettingsPage() {
               placeholder="What does this workspace focus on?"
             />
           </div>
+          <div>
+            <label className="text-xs font-medium text-muted-foreground">
+              Context
+            </label>
+            <textarea
+              value={context}
+              onChange={(e) => setContext(e.target.value)}
+              rows={4}
+              disabled={!canManageWorkspace}
+              className="mt-1 w-full rounded-md border bg-background px-3 py-2 text-sm focus:outline-none focus:ring-2 focus:ring-ring resize-none"
+              placeholder="Background information and context for AI agents working in this workspace"
+            />
+          </div>
           <div>
             <label className="text-xs font-medium text-muted-foreground">
               Slug

apps/web/lib/auth-context.test.tsx

@@ -44,6 +44,7 @@ const mockWorkspace: Workspace = {
   name: "Test WS",
   slug: "test",
   description: null,
+  context: null,
   settings: {},
   created_at: "2026-01-01T00:00:00Z",
   updated_at: "2026-01-01T00:00:00Z",
@@ -322,6 +323,7 @@ describe("AuthContext", () => {
       name: "Second WS",
       slug: "second",
       description: null,
+      context: null,
       settings: {},
       created_at: "2026-01-01T00:00:00Z",
       updated_at: "2026-01-01T00:00:00Z",
@@ -374,6 +376,7 @@ describe("AuthContext", () => {
       name: "New WS",
       slug: "new-ws",
       description: null,
+      context: null,
       settings: {},
       created_at: "2026-01-01T00:00:00Z",
       updated_at: "2026-01-01T00:00:00Z",
@@ -407,6 +410,7 @@ describe("AuthContext", () => {
       name: "Second WS",
       slug: "second",
       description: null,
+      context: null,
       settings: {},
       created_at: "2026-01-01T00:00:00Z",
       updated_at: "2026-01-01T00:00:00Z",

apps/web/test/helpers.tsx

@@ -19,6 +19,7 @@ export const mockWorkspace: Workspace = {
   name: "Test Workspace",
   slug: "test-ws",
   description: "A test workspace",
+  context: null,
   settings: {},
   created_at: "2026-01-01T00:00:00Z",
   updated_at: "2026-01-01T00:00:00Z",