Is there an Arduino library that uses ARP to get list of connected devices on network? I have been looking for a library that can execute an ARP (Address Resolution Protocol) command to return a list of connected devices on the network. The idea is that it would send the request to the gateway and get a list of MAC addresses of currently connected devices as a sort of "who's home" request.

I have searched around Arduino's libraries and have not found any that specifically perform this type of functionality so I was hoping that maybe it was available in a function within a broader networking library.

The particular networking interface (wifi via ESP8266/ESP32 or Ethernet) does not matter as I have not chosen a specific board for the job yet. I'm interested in any library solution that would allow me to poll the gateway to see which devices are currently online without having to buy a special device like FingBox.

Any recommendations for a library that includes this functionality or an approach that would allow me to send ARP commands over the network?
ARP isn't generally used the way you described. Per the spec, to resolve an IP address into a MAC address, you broadcast an ARP request for the IP address, and receive  a unicast response from the host whose address it is - not a router. It also only resolves a single IP address in one request; it doesn't return the contents of the entire ARP cache.

While you could potentially unicast ARP requests to a router, it's anybody's guess as to whether the router would respond - it's not required to. By spec only the computer who's IP address is being queried should respond - so a router should not unless you've sent it an ARP request for its IP address. You'd also have to send one request for each IP address in the range specified by the LAN's network mask.

You're better off using SNMP, if the router supports it. SNMP can read the router's entire ARP cache with very little overhead (and very few packet exchanges).

The are SNMP implementations for the ESP32 and ESP8266, but they're likely to be difficult to use. Googling will find them for you.