You could configure BIOS/UEFI to power-on when power is restored (or return to last state). Or use wake-on-LAN, which quite a few consumer routers can send through their web interface.

WoL is LAN specific, unreliable, and sometimes needs extra wires. Last state and a network-managed PDU/UPS us all you need.

Don't your servers already have BMCs supporting IPMI to provide full remote management? Often features like full KVM will require extra licensing, but remote power on is one of the most basic features and I've never encountered a BMC that didn't provide at least that much remote control.

It likely depends on the mfgr. Supermicro calls it SFT-OOB-LIC. HP has standard and advanced iLO. Haven't tried the IPMI interface on Supermicro without a license, but basic power operation might work.

I've used several Supermicro boards across several generations, and never needed the extra license key for remote power on capability. Every server BMC I've ever used from any vendor had that capability standard without requiring the premium option. The features gated behind an extra license are typically things like remote KVM or remote changing of BIOS options.

Sounds like you might need a UPS/Battery backup for outages.

Some of those servers can have multiple power supplies for failover too. They also can have cards in them to power them on/off remotely as well as long as they have power.

Use a network-managed PDU or UPS, and set systems to always power on on power restore. With that, you don't need iLO or BMC and can use in-band, host-based remote desktop.