FWIW, I also have a 16" MBP and I've also had a ton of problems with Bluetooth on this thing.
I've noticed that Bluetooth connectivity is significantly worse when the laptop is closed. You might see if keeping it open helps.
Resetting the Bluetooth module also helped resolve some persistent connectivity problems I was having (shift+option+click on the Bluetooth menubar item; choose "reset" from the menu).
Eventually this thing started having kernel panics every time I plugged something into a USB-C port and I had to send it back for replacement. Not a great experience.
I've noticed that Bluetooth connectivity is significantly worse when the laptop is closed. You might see if keeping it open helps.
Resetting the Bluetooth module also helped resolve some persistent connectivity problems I was having (shift+option+click on the Bluetooth menubar item; choose "reset" from the menu).
Eventually this thing started having kernel panics every time I plugged something into a USB-C port and I had to send it back for replacement. Not a great experience.