Oh, I was testing Paper in this clip, but tested with vanilla also. I want to reopen the issue, as this is not resolved, and invalid. Same happens in vanilla also.
I was using the standard Minecraft Launcher, and the standard Minecraft server provided by mojang. No further modifications done by me, no plugins, nothing. The client is the standard minecraft client, unmodified, only using the CavesAndCliffs datapack what also provided by Mojang. Not a large server, only a private dedicated server for 2 people, me and my friend.
Tested again, cannot reproduce either, works now, for some unknown reason.
Maybe I was generated the world before the server.properties was exist and set to hardcore, then it kept the playerdata also on server side, even if I generated a new map.
So I setted up a server.properties BEFORE started even a minecraft server, not after, then works fine.
Sorry for my incovenience.
Can be closed now.