Sure, Putin doesn't own it out right (that we know of - who knows whose LLCs have financed Musk or anyone else, really.) If he did, he'd be asked to divest a-la ByteDance.
Just in the metaphorical sense, which seems to work better too. He has perfected a system of crony tycoons.
It's an alt-right ecosystem that Musk is building, and it definitely strokes Putin's balls the right way, so far -- that's for sure.
But that doesn't make it Putin's asset, per se.