From the headline-linked Apple support page:
CR2032 batteries with bitterant coatings might not work with AirTag or other battery-powered products, depending on the alignment of the coating in relation to the battery contacts.
Bitterant coatings? They are added to small things (like button cell batteries) to make them less attractive to children. If a kid smells a bitterant coating, it’ll smell bad. If they put a bitterant coated battery in their mouth, they’ll likely spit it right out.
And it turns out that the bitterant coating can interfere with electrical conductivity. So check the package if you’re looking for a replacement CR2032 for your AirTags.
[H/T Jack Brewster]