How does bluetooth volume handling work?

My understanding of bluetooth receivers is that the sending device sends a standardised signal to the receiver on a scale from low to full (rather than arbitrary volume commands). i.e. full volume on a laptop will equate to full volume on the amp.

Is this correct? And if so, why is my speaker significantly quieter on a phone's full volume vs a laptop's full volume (tested with several)?

Also, I can't get the most out of my speaker, reducing power from 19.8v to 12v while at full volume sees no reduction in dBs, no clipping and no distortion.

Basically, I'm struggling to get the full dBs my speaker and presumably amp can handle.

I have a bluetooth enabled Wondom JA31182 amp.

Bonus questions, the JA31182 has the option to attach a potentiometer - presumably if I don't connect the potentiometer gain is automatically at 100%?