Question about a live event

I’m trying to find the key words to describe what I want to accomplish, so if you all can help me out, that would be awesome.

I’m trying to get a live event going for an anniversary party. I have my RB and gear from my PS5, I want to output signal to a TV for the live band to view and enjoy. But that same signal, I would like to output it to a video projector for the audience to enjoy. Finally, I would like the sound to come out of some speakers I’ve got set up.

Maybe I’m overthinking the set up, or maybe it cannot be done, but any thoughts or tips on this? Also, if anyone can link me a previous thread on this happening, I’m sure this question has been asked, but like I said, I’m at a loss for the key words I should be using on the search bar. Thanks to everyone for the help!