We’re running our mains to a matrix, along with a aux to raise the levels of our speaking mics. That matrix is assigned to output 29/30 and goes to our Livestream feed. Problem is, the matrix includes the reverb and delay that have been added to our vocalists’ (non-speaking) mics.
I’d do it with an Aux Mix. Stereo Aux. then select the Aux then turn down any FX returns to it. You could set the aux faders to post and all to 0 to follow the main mix but some adjustments for the Livestream can be tweaked on that. Like music up some if needed. Vocals down some to offset stage volume if you have amps and drums. Monitor with good headphones if you can’t isolate yourself. Experiment till you get it right. Save that scene setup.