What you may find is that in the past it has been recommended not to apply another screen protector over a factory fitted screen protector due to issues then with screen sensitivity as you've correctly indicated yourself.
For example I use a Whitestone Dome Glass Screen Protector and they also recommend to remove the factory fitted tpu screen protector before applying theirs.
Personally going from past information on sites I wouldn't advise to remove the factory fitted screen protector on the flip³ or fold³ @RickZie
Daily Driver > Samsung Galaxy s²² Ultra 256Gb in Phantom Black.
The advice I offer is my own and does not represent Samsung’s position.
I have no affiliation with Samsung.