Error during login to new MySQL 8 server

I just installed the new version of MySQL 8. When I try to open the connection I receive the error message: "Authentication plugin 'caching_sha2_password' cannot be loaded".

Is this related to the new MySQL version or to my installation?

You must change your user:

ALTER USER 'user'@'host' IDENTIFIED WITH mysql_native_password BY 'YourPassword';

This ist not what I want to do, at least not as a permanent solution. As far as I understand the 'caching_sha2_password' is the new standard for login, so it would be nice if HeidiSQL could handle those connections.

Yes, true. For moment when HeidiSQL get new libmysqlclient with support new authentication.