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Like literally all mobile (4/5G) internet connections are behind CGNAT, as is Starlink for example.

For landline internet connections it is indeed uncommon.

If it is really only a private server for your friends, and they are not completely computer illiterate, then a Wireguard VPN or similar seems like the safest option.

But generally speaking it isn’t that big of a deal to temporarily open a port and forward it to a game server if you want to play a round online.

A VPS is not really cost effective for that kind of usage. Maybe one with hourly billing like this: https://tierhive.com/

The exact issue that was finally fixed in the above release caused Conduwuinity to fail federation all the time. Synapse never had that issue. Yes, Synapse sucks in other ways, but be careful to think the grass is greener on the other side.