They are never cheap to operate. They got out of DC for a reason.

Few modern ones (on Intel side, AMD seems to be terrible with idle power usage) are not too bad but get something old and you'd be seeing 100W+ constant usage

This is a salient point. Any tips on hardware I could buy or build that can run many containers or VMs with variable power?

The ultra small form factor PCs that have become popular in the business market are honestly great for this. Many times they're using laptop CPUs, which significantly shrink their TDP, leading to less heat waste and power consumption while still having all the good accelerators folks desire for many homelab concerns (video codec accelerators for home media servers, VT-x/d for virtualization acceleration, etc). Grabbing three of those and installing a healthy amount of local storage and RAM and/or using a NAS for decentralized storage will get most homelabbers a real long way to doing nearly anything they want to do, and allow for simple and reliable high availability configs if you're like me and your homelab projects suddenly creep into being production systems.

I don't know what kind and how many VMs are you planning to run, but simple desktop hardware can go a long way. And they scale back power usage nicely too, when not utilized. My setup is small and old, I run an AMD FX-6100 with 20 gigs of RAM, six hard drives and an SSD, and idle power draw is around 15W.