Is the dropping of the copula (forms of 'to be') not a thing in Czech, like it is in Russian for example?
Looks so. Instead, subject pronouns are dropped usually, unless there's emphasis on them.
Czech and Russian learner here.
In Czech the copula "je" is not omitted as it is in Russian.
What about "Jseš Žofie"?
Contrary to popular belief, "jseš" is not a word in Czech at all. It is what we call "super grammar". A lot of native speakers use it when they are attempting to write in proper Czech. Overkill.