I use both methods during most events - mostly on-camera flash bounced off the ceiling if it's suitable. If the venue allows, and I know where they'll be standing most of the time: a couple of speed-lights on sticks bounced off the ceiling near those positions, or with small soft-boxes aimed directly at them. In these examples, the first image is a 32 bit raw made from 2 bracketed exposures 3 stops apart and mixed in Lightroom. I only use this method for the more posed shots like this, and the third example shows the same technique but with just one exposure. Blending the data from 2 raw files gives enormous range for adjusting the shadows and highlights. However - just having enormous dynamic image won't do anything for the *quality* of the light - only the quantity (ie the balance between screen and light on subject). Here it was pretty good, with 6 Fresnel focused warm LED spots aimed at the group from ceiling mounted light rails at the ends of the auditorium. Even so, their faces look a bit flat.
The second image is taken with the on camera flash, bounced up into the ceiling (so the light source - ie where the subject sees the light coming from, is away from the camera).. I keep a BFT* on the flash to stop any light from travelling directly forwards. Now I have a large soft light source directly over head and in front of them - and not only is there now more light on them, but the direction and shadow quality has changed too. It's also a cooler temp, but in this case I didn't bother correcting that as the flash lit the visible environment as well. And the key bit that Garry mentioned: those screens are near perfect mirrors, and the ceiling is not visible as a reflection in them, so I knew my ball of light would not show up in the screens. I would have maybe liked to shoot from a lower position, but then the ceiling *would* start to show up, reflected in the screens. The flash has reduced the contrast a bit on the screens, as it bounces about the scene - and therefore hits the screens at various angles, but it's still clear. Projector screens are more of a matt affair designed to bounce the light off in many directions, so you will probably get a larger reduction in contrast, however I don't think I would change my approach, although if they were in front of a projected image, the image would also be all over them, so that isn't a scenario that happens tbh - I would expect the presenters to be off to the side of projected image where you have the option of adding a controlled light. You can control it by increasing the ratio of distance between light-->subject and light--background (just as you would in the studio to make the background darker), and flagging it off unwanted areas.
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*BFT - Black Foamie Thing
https://neilvn.com/tangents/about/black-foamie-thing/