Bluetooth audio is a deep topic with loads of implementation specific caveats. In short, your FLACs are certainly being re-encoded to a different codec, but the good news is you are only going through one lossy conversion with FLAC.

This article covers it pretty well:
https://9to5mac.com/2018/12/31/bluetooth-audio-codecs-explained/

Depending on the source you are streaming from you may have to go to great lengths to get the best results. For example, iPhones don't support aptX at all, but if you are streaming Apple Music it can go AAC all the way through.