as far as i understand in papers people put all the losses together.
however, in implementation the do it separately.
Similar for the original gan that they put all the losses as a min max loss but in training they do backward first for discriminator and update the weights in discriminator and then do it for generator and update the weights in generator.
also based on my experience it does not really matter if you do backward for each separately comparing to the case that you sum them and then do backward on all of them.