Can't comment on the Bluetooth issue, since Apple devices have the least BT issues for me by far. But for screen recording there's the cmd+shift+5 shortcut (or the Screenshot App) to do the same thing without opening Quicktime player.
It is the only platform giving these bluetooth headaches and the reason my nice BT headset sat in the closet for almost a year.
Regarding the screenshots, I've just learned these shortcuts, but if I open the screenshot tool using CMD + Spacebar + "screenshot", it often just defaults to screen recording and I see no option to switch that.
