It takes some significant oomph to route a gigabit. if your application requires some sort of interactivity, then even more so as you'll possibly want SQM.
The lowest end thing I'd consider would be the RPi 4 which I benchmarked recently. But I'd have concerns about that setup in a remote location mainly regarding the usb ethernet dongle, and the tendency for people to not take this seriously as an important piece of hardware (so maybe to drop it on the floor or etc). If you feel like you're going to have good "remote hands" who could reset things without dropping them off the rack or whatever, then it could work ok. You could probably do it as a 1U tray, and some velcro tape to keep it in place, along with a switch that you'll want to have, and maybe even have a second unit in there that could be swapped in if there's a failure (cheap enough). I've been running it as my main router for a symmetric gigabit GPON link, and have never needed to restart it or touch it in any way, but then I don't need to drive an hour and key-card into a locked cabinet in order to restart it if I do have a problem.
You might think about just running the router in a VM on one of your existing machines, and maybe look at using keepalived to fail-over to other VMs... Basically all your servers could have OpenWrt running in a VM but only one of them would be active at any time. Any server that dies, the next highest priority machine takes over routing. I think that's what I'd look at, since it sounds like you have plenty of hardware on these machines.
You'll want to budget space for a decent rack mounted switch. Something like the TP-Link jetstream T-2600G maybe? In fact, that device can do the routing itself for ipv4.