Hello @neekoslee
Just to be clear, the Ethernet run to your outbuilding originates in the LAN Ethernet port on the primary Google WiFi unit in the main house, right? It's not connected directly to the AT&T router (which would cause problems unless you set it up as an independent primary rather than as a secondary).
All of that said, any time I see an Ethernet-connected system drop from high speed to just under 100Mbps, I immediately suspect the cable itself, or possible one of the ports it is connected to on one end or the other. If that connection can no longer reliably negotiate a 1Gbps connection, it may fall back to 100Mbps instead, resulting in the kind of performance you're seeing. So, I would start testing that cable, or even just reseating each end a few times to verify it's still working properly at 1Gbps.
I would also advise using inexpensive unmanaged Ethernet switches on each end of any long cable runs like this – especially any runs that go between buildings. Lightning strikes in the area can cause trouble for things connected to long Ethernet cables, and it's a lot easier (and cheaper) to replace a couple of $20 Ethernet switches than to replace one or more expensive WiFi router/access points.
I hope some of this helps!
