I run a home server with an i5-4590 and I haven’t seen it use more than 35W. I’m still looking to upgrade to a newer but lower power CPU (ideally one of those super low wattage chips with similar or better performance like an R7 5700U or i7-1260U).
If power usage is a concern and you don’t need much raw compute, a Pi (or similar SBC) should serve your needs just fine.
If you need a decent middle ground, take a look at mini PCs, they tend to use efficiency-focused laptop chips which are way more powerful than an SBC but sip power compared to a full-fat system.