feat: add Open WebUI AI chat integration and widget

Adds a new "openWebUi" integration kind (under a new "ai" category) and an
AI Chat widget for chatting with models served by Open WebUI.

- Integration: Bearer API key auth, model list, native chat history CRUD, and
  token-by-token streaming chat completions (SSE).
- Widget: in-input model picker, streaming responses, and an in-widget history
  panel. Reconstructs conversations from Open WebUI's message tree with a flat
  fallback.
- Streaming is delivered over the WebSocket subscription link.
- Adds integration and widget documentation.

packages/request-handler/src/open-webui.ts

@@ -0,0 +1,45 @@
+import dayjs from "dayjs";
+
+import { createIntegrationAsync } from "@homarr/integrations";
+import type { OpenWebUiChat, OpenWebUiChatListItem, OpenWebUiModel } from "@homarr/integrations/types";
+
+import { createCachedIntegrationRequestHandler } from "./lib/cached-integration-request-handler";
+
+export const openWebUiModelsRequestHandler = createCachedIntegrationRequestHandler<
+  OpenWebUiModel[],
+  "openWebUi",
+  Record<string, never>
+>({
+  async requestAsync(integration) {
+    const integrationInstance = await createIntegrationAsync(integration);
+    return await integrationInstance.getModelsAsync();
+  },
+  cacheDuration: dayjs.duration(5, "minutes"),
+  queryKey: "openWebUiModels",
+});
+
+export const openWebUiChatsRequestHandler = createCachedIntegrationRequestHandler<
+  OpenWebUiChatListItem[],
+  "openWebUi",
+  Record<string, never>
+>({
+  async requestAsync(integration) {
+    const integrationInstance = await createIntegrationAsync(integration);
+    return await integrationInstance.listChatsAsync();
+  },
+  cacheDuration: dayjs.duration(15, "seconds"),
+  queryKey: "openWebUiChats",
+});
+
+export const openWebUiChatRequestHandler = createCachedIntegrationRequestHandler<
+  OpenWebUiChat,
+  "openWebUi",
+  { chatId: string }
+>({
+  async requestAsync(integration, input) {
+    const integrationInstance = await createIntegrationAsync(integration);
+    return await integrationInstance.getChatAsync(input.chatId);
+  },
+  cacheDuration: dayjs.duration(15, "seconds"),
+  queryKey: "openWebUiChat",
+});