Broadband use requires SMS authentication. Is there any router that can successfully authenticate on the router side and devices connected to the router network do not need to be authenticated?

Maybe I don’t know enough. I have never seen or heard that broadband requires separate SMS + webpage verification when using it.

Unless it is the WIFI you are connected to, some WIFI Only if there is a verification function, you need to verify it, otherwise the optical modem or dedicated line does not require verification

If you are talking about WIFI verification, just turn off this function in the routing