What ports does Conan Exiles (Dedicated Server) use?
Conan Exiles (Dedicated Server) listens on UDP 7777. That is what has to reach the machine you're configuring: the port forward on its router, and what the firewall prompt on first launch is asking for.
UDP 7777— inbound, to the machine running the server.
If that machine is your own PC, you can skip the port forward: in Checkpoint64, Checkpoint Connect shares the running server with your team, and they join directly when they can and through a relay when they can't.
Ports are the half of hosting that happens on the router. The other half is on disk — the rule set this server reads at startup, kept in its config folder, which nothing else holds a copy of. Checkpoint64 backs that folder up automatically and keeps every version, so rebuilding the box doesn't mean rebuilding the config. And if keeping it running stops being worth it, a small group can pass one world between them instead: the dedicated server alternative guide walks through it.