Hi,
I'm sorry for the long delay. We finally found the issue with why emails were not always being sent out by these forums.
The display appears to be connected to the Internet correctly. We can tell because it is successfully reaching both DNS servers and has also received messages such as a completed a speed test showing about 44 Mbps download and 41 Mbps upload.
The red gateway warning is most likely a false alarm caused by how the display checks the gateway. The display tries to make a connection to the gateway using a few common network services. The Eero or TP-Link gateway may simply not allow those particular connections, even though it is otherwise working perfectly.
So this does not appear to mean the gateway or Internet connection is actually down. It is more likely that this particular network setup doesn't respond to the type of gateway test the display currently uses.
We could adjust how the display performs that test so it handles networks like this correctly but I'm not sure how we would get an update to you and this device has already been discontinued for a much improved version.
The display is working if you can live without it being able to determine your gateway.
The important question is whether the Eero is in bridge mode or router mode. That determines whether the display sees the Eero or the TP-Link as its default gateway.