Just get some green lentils from the bulk section. Lentils are high in zinc and It's always better to get your nutrition from actual food, rather than supplements which are unregulated and contain god knows what (not to mention it's not how your body normaly absorbs nutrients).
As far as I know, zinc pyrithione isn't available in any consumer product, because it is pretty toxic in moderate levels. Without it (from the article) "the concentration of free Zn2+ is maintained at a relatively low level by metallothioneins".
Zinc supplementation may of course help if you are deficient, but the study can't really tell if 'healthy' Zn2+ concentrations contribute anything to the inhibition of viral replication.
There's not really such a thing as 'boosting' your immune system - it's either working properly, or it's not. A 'boosted' / over-active immune system results in auto-immune diseases like Crohn's (which is what I have). Funnily enough I'm being treated with Stelara which actually suppresses my immune system - so it's no 'live' vaccines for me and other vaccines might not work effectively or at all, and I need to be extra careful to avoid getting ill. Working 100% remote is something I am appreciating more and more currently.