For my part, if they are truly socialist not just by name but have plans for a socialist governing on top of seeking for self-determination after being locked in Ukraine, they have my support BUT i fear that they might be just socialist by name and just end up becoming part of the russian federation which in that case would obviously strip any leftist of the will to support their movement. But i have to admit that i haven’t done much research on this topic.
IMO they probably only chose the “People’s Republics” names to propagate the idea that they are founded by a revolution of actual people against the Ukranian government, and because of Soviet nostalgia. Also, Russia already enacted the law to annex both republics.