I have 4 floors in my house and my connection comes into the basement and I have my current router here.
It is possible to connect a secondary Google WiFi unit back to the primary (router+firewall) Google WiFi unit via Ethernet. But, it has to be connected to the primary unit's LAN Ethernet port – you can't connect it to the same "outer" network that the primary Google WiFi unit is connected to. Here's a more detailed support document: https://support.google.com/googlenest/answer/7215624?hl=en
When you connect it this way, it will be part of the same network (same network name / SSID and password), and for any client devices that support the 802.11k and 802.11v standards, devices should hand off nicely between the access points (and between the 2.4GHz and 5GHz bands) as they move around the house.