Hi,
I just tested in my car and I can only hear BT sound on Right side. Unfortunately it is same with iPod, Tablet, MMA, Google Music, power player, ...

I have also tempered with Dev Options on my Moto X4 without success only right front speaker is heard :(

Here is some info if you want to temper with Developers options https://habr.com/en/post/456182/

Will investigate more.

EDIT:
Based on some feedback even in Settings -> Accessibility -> Hearing you have Mono disabled you have problem, it is said that these steps help:
1 - Connect with bluetooth and hear sound is not ok.
2 - Insert sound cable when it is playing hear sound ok
3 - When playing audio remove sound cable
4 - Power off/on headphones and reconnect bluetooth

Should be ok now.

EDIT 2: I have also tested with my Motorola BT headphones and Some unknown ones and one BT speaker No Issues at all music is played on both ears.

Never heard of that. Is only MMA affected by this?

Send a debug log from About right after you experience this and reply here with the logID.

MM Android V 1.3.8.0916
Motorola Moto G6 Play Android 9
Anker Soundcore Life P2 BT earbuds & OneAudio A3 BT headphones

After the first track played (any track), or if a notification received on the phone, the signal to the left ear is lost. This happens on both BT devices. By going back to the track listing and playing/restarting the track (or any track) this re-establishes the left ear signal and the song plays normally until the next track which loses the left ear again (and subsequent tracks). The only exception is after the final track - the first track will play again through both ears (left ear will then be lost again on track 2).

Would appreciate any help to resolve this. Thanks.