fix(openapi): openapi document empty (#5579)

Co-authored-by: Copilot <copilot@github.com>

packages/api/src/open-api.ts

@@ -2,10 +2,21 @@ import { generateOpenApiDocument } from "trpc-to-openapi";
 
 import { API_KEY_HEADER_NAME } from "@homarr/auth/api-key";
 
-import { appRouter } from "./root";
+import { appRouter } from "./router/app";
+import { infoRouter } from "./router/info";
+import { inviteRouter } from "./router/invite";
+import { userRouter } from "./router/user";
+import { createTRPCRouter } from "./trpc";
+
+export const openApiRouter = createTRPCRouter({
+  appRouter,
+  infoRouter,
+  inviteRouter,
+  userRouter,
+});
 
 export const openApiDocument = (base: string) =>
-  generateOpenApiDocument(appRouter, {
+  generateOpenApiDocument(openApiRouter, {
     title: "Homarr API documentation",
     version: "1.0.0",
     baseUrl: base,