I've been trying to figure out if other people get this too! Finally I'm able to corroborate this. Never thought of it as chalky, to me it's indescribable in a way that one might attempt to approximate with such a word.
Not related to caffeine pills though, I get it from caffeine itself.
Are they pure or adulturated with calcium? Most of the caffeine pills I've spotted are not just caffeine and I think this is the chalkiness you would be experiencing.
I found coffee drinking + mask wearing pretty cumbersome during the situation, and I was surprised they still make No-Doz. Seemed like something that would have been regulated away by now. Don't notice any chalkiness though.
Not related to caffeine pills though, I get it from caffeine itself.