I can't connect to my server via public search, although everything works fine when connecting directly via port and IPv4 ADDRESS

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1

when i try to connect i also get error 10061

2

You may not be able to join your own server via your public ip (server list), due to the lack of nat loopback.
You can see if your server works properly for other people joining via the serverlist with the help of this guide Port Forwarding - BeamMP Docs.