Also if you have your own net filter like PiHole or AdGuard Home with DNS rewrites set up, and you use it as a DNS server in WiFi settings, then it works a small bit differently. (I need to do this because my current ISP removed their DNS settings page for the new model). A public IP and NAT routing is never needed, as the device contacts the DNS server via the router Access Point, and the DNS server translates the service's FQDN into its internal IP. Aside from that, provided everything is set up correctly, all actual data packets go from device ←→ router ←→ service. If the router lost connection to the Internet this wouldn't break communications.