Multiple Input/Output switch (matrix?)

[TheCRODONN]

I am hoping there is something out there for me for this but i really have no idea and I will do my best to explain.

I live in a two story house and i have a 6 month old child.  My computer and xbox is upstairs.  I have a tv and monitor upstairs along with a tv downstairs.  I have a long hdmi cable running from my xbox upstairs to downstairs.  I also occasionally switch it to my computer so we can view some things easier on the tv(out of market sports games) that although my tv is wireless display capable, it does not work very well and the website does not support casting from phone/tablet.  I would like to easily play my xbox both up and downstairs without having to physically switch the cable and it would be nice to have the capability with my computer as well.  I know an hdmi switch does 1 output to 2+ outputs but is there something(even if a bit expensive), would allow me to say use xbox downstairs and then press a button or two and have it use computer downstairs and then switch it xbox upstairs?  I just may be asking way too much here but thought I would ask.  I searched amazon and saw a few products but unsure if they are what i need.  Link posted below.

Note that for my computer, i plan to just use duplicate display setting and keep my monitor plugged in while using it downstairs.  

https://www.amazon.com/FERRISA-Switcher-Splitter-Optical-Extractor/dp/B0B8Y4WH1V/ref=sr_1_15?hvadid=557460625428&hvdev=c&hvlocphy=9015722&hvnetw=g&hvqmt=e&hvrand=7891432639597659507&hvtargid=kwd-301821584348&hydadcr=18913_13357727&keywords=hdmi%2Bswitch%2B2%2Bin%2B2%2Bout&qid=1706568277&sr=8-15&th=1