I kinda assumed that was the way it was with all the teams, just because large companies are always playing with multiple shells to sleaze out of taxes and liability. Does Mercedes the car company = Mercedes F1?
I'm probably not speaking clearly because I don't see that as impacting the marketing angle. Even with Ford and Chevy and stock car racing nobody actually believes you can buy the vroom vroom used in the TV race when you go down to your local criminal syndicate dealership. But the BIRG still works its NASCAR magic.
Shell companies or not, Aston Martin the car company has nothing to do with Aston Martin the F1 team.
Mercedes F1 is 1/3 owned by Mercedes the car company, 1/3 owned by a main sponsor, Ineos, and 1/3 owned by Toto Wolff.
Ferrari F1 of course is 100% owned by Ferrari the car company (which itself is owned by FIAT).
GM does not own a single share of the new Cadillac F1 team; it's a sponsorship deal and supposedly one day an engine deal.
McLaren I've lost track of. I believe the McLaren car company has been separated from the McLaren F1 team, and there is no longer a business relationship there. But I may not be 100% correct on that.
Sauber, now Audi, is majority (I don't know how much, maybe even 100%), by the VW Group under the Audi division.
Alpine F1 majority owner is Renault the car company (who uses the name Alpine on the racing cars for marketing reasons, like GM using Cadillac as their name) and thus has the final decision making power, but they also have a lot of other minor (and not so minor) investors. Renault is majority owned by the French government.
The other teams are what could be phrased as independents, or using your NASCAR example.