Will depend on the client used. Even with UDP when the client does a connection, it will look up the ip pointing to the hostname via a DNS lookup, then try sending packets. So if the client is crap, it might never retry the lookup after XXX failed retries / time. In that case the user should see “oh the connection is down, let me cycle in the app the connection button”.

There are a lot of wireguard client implementations that act differently. I use TunSafe on Windows and it usually can retry even when changing network (wifi to lan etc).