KVM over IP would allow you to use your computer as if it was in the same room as you, if you want to control the computer from multiple rooms you’ll want to find what is referred to as a one-to-many KVM, meaning one source to many receivers.
Something like:
https://www.orei.com/products/hdmi-extender-over-cat6-7-with-kvm-hdmi-loop-out-1080p-60hz-up-to-330-ft-ex-330-kvm

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Using terminals, thin clients, or low powered machines at the end points would require setting up Windows RDP or running some level of virtualization with Microsoft Hyper-V either of which would require Windows Server to operate effectively. Last I checked Windows Hyper-V does no support GPU pass through.

KVM over IP would allow you to control the computer from another room given that are able to run a dedicated Ethernet connection between the two rooms. There are some rated for 4k@60Hz which would allow you to get some lightweight gaming.

Sine wave is a newer marketing push but for most home labs and DIY data hoarding it’s not needed,

If you plan on running higher end enterprise grade storage solutions or equipment that is very sensitive to power fluctuations the an online UPS would be needed.

For most of us and for the hardware you’ve listed any line-interactive sine or no sine way UPS will do you just fine. Just do your homework on power draw and expected run time and you’ll be fine.