If the difference between right and left is at it's heart an overall preference for either tradition or change, the free market has always been forward-looking, innovation seeking, and focused on the next big thing. It's never been static and is in a constant state of change. The market isn't a thing or a place, it's a process of discovery, constantly striving to be more efficient at giving people what they want in increasingly complex and creative ways. Destruction of old ways of doing things in order to pivot to something better, liquidation of malinvestment and creative destruction, is part of that process.
Like... if "right wing" in America is a lean towards tradition over change, one could say the market is right wing only in the sense that historically, we had a freer market than most other nations with a founding inspired in part by classical liberals like Adam Smith and John Locke. The political right at least claimed until recently a desire to return to that tradition, when we've drifted so far from that with regulatory capture towards more centralized control and restrictions of individuals and groups of individuals insulating them from that process of discovery. But that tradition we've largely turned our back on as a nation functions in a way that's left wing and constantly discards tradition in practice.
In America, the free market is a tradition of change that draws from the best of the right and the best of the left simultaneously.