The problem I had is that I need the "AllowedIPs = 0.0.0.0/0" since I want to be able to serve traffic "from everywhere" (federation FTW!). Unfortunately, when using 'wg-quick' it means that it will set up special routing rules to redirect *all* (even outgoing) traffic through Wireguard, and thus VPS. I noticed when Steam downloads became slow :) (yes, this server is also a gaming machine).
What ended up working is a) Setting "Table = off" in the Wireguard config, not to create the "move all traffic through Wireguard" routing rules, b) manually route traffic coming from wg0: "ip route add default via $WG0_IP dev wg0 table 1000; ip rule add from $WG0_IP table 1000"
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