Is there any program to draw on the screen during full screen presentations via Zoom? Device: MacBook Air

I am holding a presentation and want to write (with a Wacom graphic tablet) on the screen while presenting. My slides are created in Keynote, but I can use the exported .pdf document as well. So far I've tried the following: - Presentation/fullscreen mode of Keynote/Adobe/standard Mac pdf viewer and trying to comment directly via Zoom
**Problem**: instead of drawing, the next slide is displayed because my Mac thinks that I am clicking -- to circumvent this, I disabled advance on click in Keynote, but then I cannot even go to the next slide with my keyboard. - Fullscreen mode of Adobe/standard Mac pdf viewer and trying to use the built-in comment function of Adobe/smpv
**Problem**: I need to switch between presentation and drawing mode. And if I have a series of developing slides (i.e., where one bullet point becomes visible after the previous one) the drawing disappears (but I need the drawing displayed until all bullet points are displayed). I don't have any iOS device for remote presentation. (Honestly, really annoying that you can't just use the necessary features with a Mac.)