Configuring TCP-MSS ClampingConfiguring TCP-MSS Clamping in the VyOS firewall solves the problem. I suppose the WireGuard tunnel makes the maximum segment size smaller, causing PMTU discovery to fail.
https://docs.vyos.io/en/latest/routing/mss-clamp.html
set firewall options interface wg02 adjust-mss '1372'
This https://bugzilla.redhat.com/show_bug.cgi?id=1478704link is a related question with an pppoe interface, that. That discussion helped me to find the solution.