Who claimed that Denmark was socialist/communist/marxist? They have social democratic traditions sure, but like the other Scandinavian countries, they have generally transitioned to a more right-wing oriented economic policy over the last 20-30 years, while maintaining their social security net.

Is it somehow inherently socialist/communist/marxist to provide job retraining to people moving between jobs at privately owned companies?

Seems to me that it’s highly beneficial to the private companies involved.