Hold on, putin isn't left or right, he is outside of political spectrum. Even if he once was part of a country that called itself communist, there's nothing left of that expect corruption.

He only wants power, and total control just like trump, that's why trump praises him, because he wants to be him. More handsome with total control and power and more people praising him. Less regulations or opposition. That's why he has praising most authoritarians.

Putin is also a dictator who is mostly praised by far right and conservatives, as he has "traditional" values that appeals more to right wing with conservative values then left, with progressive values. He also wants to use political extremists and trolls for his gains, which ever would suite him, but mostly he aligns with values of right wingers. This confuses people to think that he is either left or right. He is outside of it, and nothing but a dictator who has personal interests in mind, not the citizens.