I think the term comes from how these regimes like to show power with tanks. It was an insult made up by a group of British trots against other European communist groups for their support of the USSR intervention in an attempted color revolution (involving a bunch of actual og nazi-affiliates/Nazis) in Hungary in the '50s. The intervention involved driving tanks into Hungary, thus “tankie”. Of course later openings of CIA archives confirmed that the revolution was indeed supported by the CIA. The nazi thing was evident at the time, you can just look up the groups involved and the participants. Like so many other leftist terms it was co-opted by liberal inteligentsia so it could seem like they had some sort of foundation for their red-scare propaganda. It since spread from there. These days it describes anyone to the left of the person using the term or anyone who dares to suggest that the invasion of Ukraine happened for more complex reasons than “Putin bad”.