Author here, indeed I didn't install a UPS. I've tried to keep my setup fairly minimal, and I'm consciously accepting that if there's a power outage my services will be down. I self-host exclusively for myself, not for others.
What I don't want though is a power outage putting my server offline while I'm on holidays, and not be able to access my services at all.
My ISP-provided router supports Wireguard, so I can use that to connect to my KVM and send the Wake on LAN packages.
Out of curiosity, did you look through the BIOS options on your computer? Mine is much less capable than yours (it is a used mini-pc) but it has options to boot itself up upon resuming power.
I use UPS for my internet and then remote access such as intel AMT will get you back into your systems if you've specced your hardware to have such features.
You REALLY should not expose AMT to the internet.
of course not, but you would vpn in, your router (or server behind your router but that may be more risky being able to get in if something fails) should run a vpn if you plan to use something like AMT.