You could use BTT's drawing gestures (or the floating menus):
https://docs.folivora.ai/docs/701_drawings.html
To set this up you'd need to trigger the "Start Recording Drawing" action on mouse-down and the "Stop Recording Drawing" action on mouse up:
The setup for floating menus would be similar, you can use the "Show Floating Menu" action on mouse-down and the "Hide Floating Menu" action on mouse up.