"WAN" ---- Router 1 ---- Router 2 ---- Router 3 ---- Router 4 ...

They have libremesh installed, only BATMAN_ADV, not BMX neither babeld, without DHCP server. Each connected client get the IP from the "WAN"

They have watchping to see if connectivity over ethernet is lost, for example cable broken between Router 1 and 2. In this case, i suppose that Router 1 and 2 are still connected through BATMAN_ADV over wifi.

Would Router 3 and 4 be workin over ethernet or over wifi?

I mean .... Router 2, 3, and 4 would have reset IP connection on ethernet because of whatchping, although Router 3 and 4 have physical connection over ethernet.