feat: add YouTube liked videos sync via OAuth 2.0

Adds OAuth 2.0 flow to connect a YouTube account and sync liked
videos as "like" posts on the blog. Includes:
- OAuth authorize/callback/disconnect flow with token persistence
- getLikedVideos() method using videos.list?myRating=like
- Background periodic sync + manual sync trigger
- Dashboard UI for connection status and sync controls
- Public JSON API for querying synced likes

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

lib/youtube-client.js

@@ -321,6 +321,65 @@ export class YouTubeClient {
     return `${minutes}:${seconds.toString().padStart(2, "0")}`;
   }
 
+  /**
+   * Make an authenticated API request using an OAuth access token.
+   * Falls back to the API‑key based `request()` when no token is given.
+   * @param {string} endpoint
+   * @param {object} params
+   * @param {string} accessToken - OAuth 2.0 access token
+   * @returns {Promise<object>}
+   */
+  async authenticatedRequest(endpoint, params = {}, accessToken) {
+    if (!accessToken) return this.request(endpoint, params);
+
+    const url = new URL(`${API_BASE}/${endpoint}`);
+    for (const [key, value] of Object.entries(params)) {
+      if (value !== undefined && value !== null) {
+        url.searchParams.set(key, String(value));
+      }
+    }
+
+    const response = await fetch(url.toString(), {
+      headers: { Authorization: `Bearer ${accessToken}` },
+    });
+
+    if (!response.ok) {
+      const error = await response.json().catch(() => ({}));
+      const message = error.error?.message || response.statusText;
+      throw new Error(`YouTube API error: ${message}`);
+    }
+
+    return response.json();
+  }
+
+  /**
+   * Get the authenticated user's liked videos.
+   * Requires an OAuth 2.0 access token with youtube.readonly scope.
+   * Uses `videos.list?myRating=like` (1 quota unit per page).
+   * @param {string} accessToken
+   * @param {number} [maxResults=50]
+   * @param {string} [pageToken]
+   * @returns {Promise<{videos: Array, nextPageToken?: string, totalResults: number}>}
+   */
+  async getLikedVideos(accessToken, maxResults = 50, pageToken) {
+    const params = {
+      part: "snippet,contentDetails,statistics",
+      myRating: "like",
+      maxResults: Math.min(maxResults, 50),
+    };
+    if (pageToken) params.pageToken = pageToken;
+
+    const data = await this.authenticatedRequest("videos", params, accessToken);
+
+    const videos = (data.items || []).map((video) => this.formatVideo(video));
+
+    return {
+      videos,
+      nextPageToken: data.nextPageToken || null,
+      totalResults: data.pageInfo?.totalResults || videos.length,
+    };
+  }
+
   /**
    * Clear all caches
    */