>SSD + HAT + PSU + Case + Cooler

Zero of any of that is needed. The new Pi "works best" with a cooler sure but at standard room temps will be fine for serving web apps and custom projects and things. You do not need an SSD. You do not need a HAT for anything.

Apparently the Pi 5 8gb is $120 though WTF.

What personal web site or web app or project can't run just fine on a Pi Zero 2 though? It's a little RAM starved but performance wise it should be sufficient.

Other than second-hand mini PCs, old laptops also make great home servers. They have built in UPS!