This is not strictly a Linux-issue as I reproduce this issue under Windows 10 as well (but can not reproduce under Android or macOS), but I will be using Linux for any troubleshooting and I wasn’t sure where else to post this....
The mx5 only support sbc (minimum to support) aac and LDAC. They dropped aptx to only use their own high latency (and not that much better) codec. The headphone has BT 5.3, but does not support LC3 (an extremely good, low latency codec integrated in base bluetooth).
Help troubleshooting issues with Sony WH1000MX5 playback
This is not strictly a Linux-issue as I reproduce this issue under Windows 10 as well (but can not reproduce under Android or macOS), but I will be using Linux for any troubleshooting and I wasn’t sure where else to post this....