I doubt it. There’s practically no market for them (nobody is particularly nostalgic for floppy disks, even in retro computing), but above all, unlike with cassette decks (where cheap manufacturers existed alongside expensive name brands), during the floppy heyday, only major companies, mostly Japanese, made them (Sony, Matsushita, Teac, Mitsumi, NEC, Alps, Samsung, Epson, Citizen, etc). I’ve never heard of a true no-name floppy drive mechanism, so there would be no such company to continue manufacturing. Not saying they definitely didn’t exist, but I’ve never come across it.
I suppose it’s possible a major company sold off its tooling when exiting the market, but who knows.
As I said above: the number of 3rd party drives has been reduced to almost zero, they’re all the same item rebadged, with my suspicion being that they’re using up drive mechanisms bought in bulk.
Floppy heads and cassette/magstripe heads are nothing alike. It’s unlikely there’s any real overlap in manufacturers. (And while cassette heads, especially good ones, are a niche product now, magstripe readers are still installed by the millions, even if only as backup for when the chip can’t be read.)