Yes, that's still exactly for free.

Free doesn’t seem like a great name for situations in which profit is extracted from a user in a sort of nebulous fashion.

you could say the same thing about ad based businesses. how else is the company supposed to cover its costs if it has a free service?

They aren’t free, they are ad funded. You pay for the service by viewing the ads.

The only organizations that provide free services are, like, donation driven charities. Or hobbyist groups.

Maybe somebody could argue for government funded organizations, but I don’t want to get into that whole can of worms.