Three general approaches.
1) Some screens will have an audio out. Damn near mythical today, especially for something other than TOSlink/spdif which few things other than big boy amps will take in, but hey. Assuming that is not the case though then many in the past have noted that the feed to the speakers is good old analogue audio, better ones still might tap it before the amp and allow a better amp to do things (though internal amps are not so bad most of the time in screens as it is the small speakers that bring the whole affair down).
Good quality and cheap (slice off an old headphone cable/aux cable and solder that in if you want, if you have to buy and glue in a 3.5mm socket then still cheap), also more future proof. Dual screens could complicate this though.
2) There is such a thing as a HDMI audio splitter and they are not all that expensive. These will do as the name implies and split off the audio signal to probably 3.5mm but bluetooth and more active approaches are available, as might be surround options for more still. That said looking at your switch then such things appear to be inbuilt, both 3.5mm and optical TOSlink/spdif (little red light if you poke the thing in, goes to a fibreoptic cable though again it is mostly going to be big boy amps that have an input for that these days, big boy amps also doing HDMI is a thing as well, though there are external options for computers)
https://cdn.shopify.com/s/files/1/1...-5dd7-4ef1-8105-4d57d4f95281.pdf?v=1649934947 mentioning it.
3) Aside from maybe the directv box all those devices should have options for separate audio out as of various updates (USB and bluetooth if nothing more analogue exists). It would be possible to get it together to take inputs individually into a switch, amp and whatnot to control things.
https://www.audio-direct.com/how-to-connect-bluetooth-headphones-to-ps5/
https://screenrant.com/nintendo-switch-audio-pc-monitor/
https://www.nintendo.co.uk/Support/...d-Manage-Bluetooth-Audio-Devices-2040147.html
https://www.directv.com/support/satellite/article/KM1010001/ mentions RCA connections so you could probably get those to 3.5mm or whatever your amp wants.
For all of those independent volume should be an option either innately as part of the setup (if the audio is going into line in on the PC then it is another input on the PC you can change happily, as will bluetooth or whatever outputs) or as part of a setup with more cheap bits (external muxers and audio switches are a thing if you don't necessarily want the PC on and controlling everything, maybe with some in line volume controls if the muxer-amp is going to be more than you care for or need a quick mute this game to take a call option).
Further to this modern HDMI can be a bit nicer for some setups by something call ARC (audio return channel) which looks like it is supported by your HDMI switch. Most computer monitors will probably not do so well with this though, not to mention if you are using the switch mentioned there to throw around signals as your whims take you then only one port supports it.
https://www.tomsguide.com/us/hdmi-arc-faq,news-26262.html for a general overview on ARC.
