refactor: move home query ID methods to mixin as private

Follow the pattern from twitter-client-timelines.ts where query ID
methods are private to the mixin that uses them, rather than protected
in the base class.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <[email protected]>

src/lib/twitter-client-base.ts

@@ -67,16 +67,6 @@ export abstract class TwitterClientBase {
     return Array.from(new Set([primary, 'M1jEez78PEfVfbQLvlWMvQ', '5h0kNbk3ii97rmfY6CdgAA', 'Tp1sewRU1AsZpBWhqCZicQ']));
   }
 
-  protected async getHomeTimelineQueryIds(): Promise<string[]> {
-    const primary = await this.getQueryId('HomeTimeline');
-    return Array.from(new Set([primary, 'edseUwk9sP5Phz__9TIRnA']));
-  }
-
-  protected async getHomeLatestTimelineQueryIds(): Promise<string[]> {
-    const primary = await this.getQueryId('HomeLatestTimeline');
-    return Array.from(new Set([primary, 'iOEZpOdfekFsxSlPQCQtPg']));
-  }
-
   protected async fetchWithTimeout(url: string, init: RequestInit): Promise<Response> {
     if (!this.timeoutMs || this.timeoutMs <= 0) {
       return fetch(url, init);

src/lib/twitter-client-home.ts

@@ -24,6 +24,16 @@ export function withHome<TBase extends AbstractConstructor<TwitterClientBase>>(
       super(...args);
     }
 
+    private async getHomeTimelineQueryIds(): Promise<string[]> {
+      const primary = await this.getQueryId('HomeTimeline');
+      return Array.from(new Set([primary, 'edseUwk9sP5Phz__9TIRnA']));
+    }
+
+    private async getHomeLatestTimelineQueryIds(): Promise<string[]> {
+      const primary = await this.getQueryId('HomeLatestTimeline');
+      return Array.from(new Set([primary, 'iOEZpOdfekFsxSlPQCQtPg']));
+    }
+
     /**
      * Get the authenticated user's "For You" home timeline
      */