I just went looking around and the zinc supplement market is kind of a mine field of shit that is not what you want...
First, it has to be zinc acetate or zinc gluconate, other zinc compounds work either poorly or not at all.
Second, additives such as citrate/citric acid, malate/malic acid, tartrate/tartaric acid, sorbitol, mannitol, or amino-acid chelators all bind to the zinc and make it not bio-available.
And there's a ton of supplements that violate one or both of those rules.
I found two options that are not too bad:
https://fr.iherb.com/pr/life-extension-enhanced-zinc-lozenges-peppermint-30-vegetarian-lozenges-18-75-mg-per-lozenge/87151This is pretty close to what was in the research, but you need to take 6 a day, so that bottle is worth 5 days...
https://www.vitabay.de/en/products/zinc-50-depot-vegane-tablettenThis is kind of not intended for the purpose, but it's cheap and high potency, and if you put it in your mouth for a while before swallowing it, you're going to get a LOT of the right kind of zinc running down your throat, so it's still interesting.