Change firebase project and setup image caching

[scorpionknifes]

💡 デスクリプション

🔨 変更内容

• change firebase project
• add image caching with lru

  これはどのようにテストされていますか

@HiruNya would be writing tests for these :P

📸 スクリーンショット

✅ チェックリスト

• [x] My code follows the style guidelines of this project
• [ ] I have performed a self-review of my own code
• [ ] I have commented my code, particularly in hard-to-understand areas
• [ ] My changes generate no new warnings
• [ ] I have added tests unit/integration that prove the changes work
• [ ] New and existing unit tests pass locally with my changes
• [x] I have checked my code and corrected any misspellings

[render[bot]]

Your Render PR Server URL is https://viral-vtubers-pr-167.onrender.com.

Follow its progress at https://dashboard.render.com/static/srv-ca07ucv5f992fsis47hg.