Nest Wifi Pro Ethernet backhaul after switch

[Teapot]

I have an AT&T gateway connected to an unmanaged Ethernet switch, sitting in a closet. The remaining ports of the switch are wired to Ethernet ports in other rooms. Is there a way to connect 3 Wifi Pro units to some of these ports and establish a mesh wifi network, i.e. they would use the Ethernet ports as backhaul. When I go through the normal installation process the wifi doesn't connect.

From what I've read elsewhere, the correct approach is Gateway > primary Nest wifi > switch > other Nest wifi units

In my case, because the Gateway and switch are in a closet I'm hoping for

Gateway > switch > primary Nest wifi & other Nest wifi units (all connected to the same switch)

Thanks much for any help!

[Tanquen]

I also have AT&T fiber and they make you user their modem and all in one WiFi/router access device. I just wanted to add a few Nest WiFi Pro for better mesh coverage. It seems to work but there are some odd things. Like if the second Nest WiFi Pro that is in bridge mode is powered off then all the WiFi devices no longer work or get an IP address even though the first Nest WiFi Pro that was setup as the router and is in NAT (standard) mode is still on line.

So I have:
AT&T Fiber Modem → AT&T Router → Unmanaged Switch → Both Nest WiFi Pros WAN port are connected to the switch.

I think that maybe the second Nest WiFi Pro should have it's WAN port directly connected to the first Nest WiFi Pros WAN port?