Interesting enough…

tcpdump -i wg0 
21:49:49.604220 IP 10.70.0.1 > dns.google: ICMP echo request, id 5337, seq 1, length 64
21:49:49.638242 IP dns.google > 10.70.0.1: ICMP echo reply, id 5337, seq 1, length 64
21:49:50.615200 IP 10.70.0.1 > dns.google: ICMP echo request, id 5337, seq 2, length 64
21:49:50.648361 IP dns.google > 10.70.0.1: ICMP echo reply, id 5337, seq 2, length 64
21:49:51.628391 IP 10.70.0.1 > dns.google: ICMP echo request, id 5337, seq 3, length 64
21:49:51.673502 IP dns.google > 10.70.0.1: ICMP echo reply, id 5337, seq 3, length 64
21:49:52.641711 IP 10.70.0.1 > dns.google: ICMP echo request, id 5337, seq 4, length 64
21:49:52.673321 IP dns.google > 10.70.0.1: ICMP echo reply, id 5337, seq 4, length 64
21:49:53.655076 IP 10.70.0.1 > dns.google: ICMP echo request, id 5337, seq 5, length 64
21:49:53.695391 IP dns.google > 10.70.0.1: ICMP echo reply, id 5337, seq 5, length 64

while on the other console, as user 1070:

 ping 8.8.8.8
PING 8.8.8.8 (8.8.8.8) 56(84) bytes of data.

just gets stuck there…

This is baffling!