Just as comment: Be aware, that the usual home cinema projectors are usually not powerful enough to create a background picture, that is really visible with some stage lighting on the band.
Home cinema beamers rely on a really dark environment. I recently bought a used business beamer like it is used for team meetings in an office (an acer with 4000 Lumen), and I found it to be the minimum.
You may check the second video in:
https://forum.critterandguitari.com/t/using-the-etc-with-video-fx/
You can see that there is not much lighting on the musicians, but still the backscreen projection is some kind of pale.