feat: add paginated API endpoint for groups (#27603)

backend-only changes from #27271; see that PR for summary of changes +
implementation details

site/src/api/typesGenerated.ts

@@ -6917,6 +6917,47 @@ export interface OrganizationSyncSettings {
 	readonly organization_assign_default: boolean;
 }
 
+// From codersdk/groups.go
+/**
+ * PaginatedGroup is a group summary returned by the paginated groups endpoint.
+ * It deliberately omits the member roster (which the endpoint does not return)
+ * and exposes only the total member count. Fetch the roster via the group
+ * members endpoint.
+ */
+export interface PaginatedGroup {
+	readonly id: string;
+	readonly name: string;
+	readonly display_name: string;
+	readonly organization_id: string;
+	/**
+	 * TotalMemberCount is the number of members in the group, shown even when
+	 * the caller cannot read individual members. The roster itself is not
+	 * returned by this endpoint.
+	 */
+	readonly total_member_count: number;
+	readonly avatar_url: string;
+	readonly quota_allowance: number;
+	readonly source: GroupSource;
+	readonly organization_name: string;
+	readonly organization_display_name: string;
+}
+
+// From codersdk/groups.go
+/**
+ * PaginatedGroupsRequest are the filters for a paginated groups request.
+ * Groups only support free-text search, so unlike UsersRequest it exposes no
+ * key:value filters that the endpoint would reject.
+ */
+export interface PaginatedGroupsRequest extends Pagination {
+	readonly q?: string;
+}
+
+// From codersdk/groups.go
+export interface PaginatedGroupsResponse {
+	readonly groups: readonly PaginatedGroup[];
+	readonly count: number;
+}
+
 // From codersdk/organizations.go
 export interface PaginatedMembersRequest {
 	readonly limit?: number;