fix(api,web): separate workspace context from auth session (#551)

Co-authored-by: Jason Woltje <jason@diversecanvas.com>
Co-committed-by: Jason Woltje <jason@diversecanvas.com>

apps/api/src/workspaces/dto/index.ts

@@ -0,0 +1 @@
+export { WorkspaceResponseDto } from "./workspace-response.dto";

apps/api/src/workspaces/dto/workspace-response.dto.ts

@@ -0,0 +1,12 @@
+import type { WorkspaceMemberRole } from "@prisma/client";
+
+/**
+ * Response DTO for a workspace the authenticated user belongs to.
+ */
+export class WorkspaceResponseDto {
+  id!: string;
+  name!: string;
+  ownerId!: string;
+  role!: WorkspaceMemberRole;
+  createdAt!: Date;
+}