His covid policy has probably been to the left of even most Democrats. With that said, I don't think he would fit neatly into either party.
Describing Covid policy in terms of "left" and "right" doesn't make any sense. I think you're falling down the classic trap of "what Democrats would do here = left" and "what Republicans would do here = right". Which makes people say things like "I'm left-wing on guns" and they mean they support gun control. There's nothing left-wing or right-wing about being for gun control or Covid lockdowns or military intervention.