The PC Engines APU2 boards are really great for this in terms of routing performance per watt, but the prices are up. If you can find a used one it might be possible. I use one for routing and a Lenovo ThinkCentre M700 tiny as a server. The M700 is around double the power consumption at idle, but they are both pretty low power. On 120v the APU2 is ~5w, and the M700 is ~10w when idle.
There are a couple of Celeron N2830 fanless mini-pc router options on aliexpress for under €100. It's 2 core vs the APU2 4 core CPU, but it's faster per-core, so it should do basic gigabit routing without too much trouble (the APU can do it with OPN/pfSense, but only with some tuning).
And that's where I think you may have some trouble. I expect OpenBSD will be slower on the network than those FreeBSD-based distributions. And they max out at gigabit on the APU2 platform. But you could always decide later to switch the OS if you need gigabit performance.