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/integrations/src/base/creator.ts

@@ -38,6 +38,7 @@ import { NavidromeIntegration } from "../navidrome/navidrome-integration";
 import { NextcloudIntegration } from "../nextcloud/nextcloud.integration";
 import { NPMIntegration } from "../npm/npm-integration";
 import { GotifyIntegration } from "../gotify/gotify-integration";
+import { OpenWebUiIntegration } from "../open-webui/open-webui-integration";
 import { NTFYIntegration } from "../ntfy/ntfy-integration";
 import { OpenMediaVaultIntegration } from "../openmediavault/openmediavault-integration";
 import { OPNsenseIntegration } from "../opnsense/opnsense-integration";
@@ -143,6 +144,7 @@ export const integrationCreators = {
   uptimeKuma: UptimeKumaIntegration,
   peaNut: PeaNutIntegration,
   beszel: BeszelIntegration,
+  openWebUi: OpenWebUiIntegration,
 } satisfies Record<IntegrationKind, IntegrationInstance | [(input: IntegrationInput) => Promise<Integration>]>;
 
 type IntegrationInstanceOfKind<TKind extends keyof typeof integrationCreators> = {