However, a used cigarette butt will additionally contain adhesives and any flavorings as well as some leftover compounds deposited by the smoke. The wikipedia article goes into higher detail on this: https://en.wikipedia.org/wiki/Cigarette_filter
Cellulose acetate is only sort-of biodegradable like Cellulose. Here is a study looking at the topic: https://link.springer.com/article/10.1007%2Fs10924-010-0258-...
> Cellulose is readily biodegraded by organisms that utilize cellulase enzymes, but due to the additional acetyl groups cellulose acetate requires the presence of esterases for the first step in biodegradation. Once partial deacetylation has been accomplished either by enzymes, or by partial chemical hydrolysis, the polymer’s cellulose backbone is readily biodegraded.
I.e. if you throw butts in an ordinary compost pile, they might not get anywhere for a while.
I agree however, that I'd rather just use re-usable glass or metal cup (with a handle or suitable insulated wrappping) and avoid the potential for hot liquids leaching things out of plastic!