Why via LAN to the AP and not directly to the router? Google Wifi makes its own network. And yes, the one on the first floor only needs power and then blends the MeshNet via WLAN.
My router is connected to the cable network modem - I have installed an access point on the ground floor, the AP is connected to the router in the basement via a LAN cable. Unfortunately, the AP does not provide enough power to operate the WLAN on the ground floor and first floor without gaps.
Can I connect one of the Google satellites on the ground floor to the AP via cable (Zyxel, third-party product) and operate the other one wirelessly on the first floor? Are these two satellites then set up as a MeshNet with smooth transition from one transmitter to the other?
A Google Wifi satellite would replace the existing AP (it forms one itself), the second satellite is connected via WLAN in the Mash network. However, it must not be too far away from the first satellite; if the connection is too weak, no connection can be established (the app asks to reduce the distance). I had the same problem, previous AP in the ground floor, no or miserable throughput in the basement and first floor. A Google Wifi on the ground floor was able to cover half of the house, but the performance was not sufficient to connect the satellite on the upper floor (reinforced concrete ceiling UG/EG/OG). My working solution: both Google Wifi installed on the ground floor with a distance of approx. 8-9 metres (virtually from one corner of the house to the other), now I have min. 30 Mbps everywhere from the ground floor to the upper floor (100 Mbps directly next to the first satellite, which is the max. of my subscribed bandwidth). Automatic handover from satellite to satellite takes place without any problems (I used to use two Devolo dLan WLAN adapters, which stuck to the first AP with poor reception even though I was standing next to the second AP; the handover here does not work as advertised by the manufacturer). My conclusion: Google Wifi fulfils its promise of a mash network, as long as you can keep to the recommended distances of the individual satellites (or add more satellites). After several attempts (Devolo dLan WLAN and several high-quality WLAN routers), finally WLAN in the whole house.