Most Bluetooth devices introduce some lag.
When you play a video from your PC or your phone, the devices compensate for the Bluetooth lag by delaying the images.
For example, when stopping a video you should notice that the sound plays for a few milliseconds after the image is stopped.
If you were to use an app that require realtime audio, you should notice a bit of lag when listening via your Bluetooth headset.
Could you retry your tests but, instead of playing a video, you use this site? Let me know if using AudioRelay introduces a bigger noticeable delay on top of the Bluetooth one.
As for fixing the issue at hand, which is have video images synchronized to the audio, it’d require to implement what’s proposed here: