Can you help out with some more specifics? What are you trying to do with this setup? Are you wanting a surround-sound setup with the sound bar serving as the L/C/R and those wall speakers as the surrounds? What brand is the soundbar? Is there a reason you want to connect the AVR to the tv?
Or are you using the soundbar alone for the tv and want to use the receiver to drive music through the speakers and the outdoor speakers? In which case I'm not sure why you'd need any connection between the TV/SB and the closet, just wire the tv to the SB (assuming the TV is a smart tv and you don't need a separate streamer). If you need a cable/satellite box, that changes things, but if you're just doing a YouTubeTV/Hulu setup, I don't think you'd need anything else.
For connectivity, if you have a cable modem located in that closet, I'd just use an ethernet router and run Cat5 directly from the router to your AVR/AppleTV. No reason to involve WiFi if you can connect directly with ethernet.