Nothing will happen as long as Parler isn't widely used in Russia. (I'm going on the assumption they're even actually hosted there.)
The Russian M.O. seems to be to maximize chaos. I don't think they care about the details very much, and I doubt Putin cares one bit what random net-dwellers outside Russia say about him. He cares about:
The words that come from the Parler CEO are very different to his actions.
It's been rumoured (with very good sources) that he happily complied with FBI requests to turn over data. So it wouldn't surprise me if was more than happy to comply with whatever Putin wanted so long as it was kept quiet.
The Russian M.O. seems to be to maximize chaos. I don't think they care about the details very much, and I doubt Putin cares one bit what random net-dwellers outside Russia say about him. He cares about:
-Control in Russia
-Making life difficult for opposing states.