Indeed, ensuring stability and image quality during mirroring has been a priority for me. While using various methods, including built-in features and third-party apps, I have experienced occasional lag and synchronization problems. However, I've recently come across a potential solution in the form of the "DoCast: Cast to Chromecast TV" app
https://apps.apple.com/us/app/docast-cast-to-chromecast-tv/id6446948344. This app boasts of reliable mirroring capabilities with minimal lag and optimal audio-video synchronization. The app's features have streamlined my mirroring experience, delivering smoother performance and higher image quality. It's worth considering such dedicated solutions to enhance the stability and quality of mirroring, especially in scenarios where seamless projection is crucial.