Ну все таки логи не бесконечные, через 540 секунд - ядро забывает об этом туннеле.
Ну а с уровнем логирование, это все к создателю WG
[I] Apr 11 18:10:21 kernel: wireguard: Wireguard0: handshake for peer "wg-key-abcd" (5) (x.x.x.x:4688) did not complete after 5 seconds, retrying (try 18)
[I] Apr 11 18:10:27 kernel: wireguard: Wireguard0: handshake for peer "wg-key-abcd" (5) (x.x.x.x:4688) did not complete after 5 seconds, retrying (try 19)
[I] Apr 11 18:10:32 kernel: wireguard: Wireguard0: handshake for peer "wg-key-abcd" (5) (x.x.x.x:4688) did not complete after 5 seconds, retrying (try 20)
[I] Apr 11 18:10:37 kernel: wireguard: Wireguard0: handshake for peer "wg-key-abcd" (5) (x.x.x.x:4688) did not complete after 20 attempts, giving up
[I] Apr 11 18:12:20 kernel: wireguard: Wireguard0: zeroing out all keys for peer "wg-key-abcd" (5) (x.x.x.x:4688), since we haven't received a new one in 540 seconds