Hello @bjacosta
Yes, you can do this. Here's a support page with more details: https://support.google.com/googlenest/answer/7215624?hl=en
But, the short version is that you will want to get the new secondary Google WiFi unit set up as a wireless mesh unit first in the house. Once it's part of the network and working, you will want to test the wired connection by connecting it (still in the house) to the LAN port on the Google WiFi primary (router). Check the detailed information for that secondary in the Google Home app to make sure it shows the connection type has changed from "mesh" to "wired". At this point, I would probably use a couple of inexpensive unmanaged Ethernet switches on either end of the long cable run between the buildings just to provide some electrical isolation. Just connect one switch to the LAN port on the primary / router Google WiFi unit, connect the house end of that long cable run to that switch, and then connect the other switch to the other end of the long cable run out in the metal building. I would then test that Ethernet cable run using a laptop or something to verify it all works properly and performs as expected (hopefully, with a good Cat 6 cable you'll be able to maintain a 1Gbps connection). Finally, unplug the new secondary Google WiFi unit and move it to the outbuilding. Connect it to the Ethernet switch out there and power it up. Check the detailed information on it again to make sure it's showing as "wired" and run a mesh test. Your client devices should be able to connect to it when they're out there, plus having that switch out there means you can connect wired devices as well.
