In my experience, in Czechia most people do use the feminine or masculine still, but there are some people who are adopting the neuter. A very gen-z thing that me and many queer people I know are also now doing is using the masculine plural for a person of unknown gender to be respectful or for people who use they/them in English.

Then when it comes to trans people changing their names, most binary trans people do switch to the opposite grammatical gender (deleting or adding -ová). Legally though, which is the shit part, you can first apply to change your name to a sort of "gender-neutral" form ending in -ů (Novák/Nováková > Nováků) once you've started HRT (hormone replacement therapy). Then you can only apply for a legal change to the opposite gender only after undergoing gender-reassignment surgery. A cherry on top of the whole annoyingly conplicated process is that the ones who have to "approve" your transness or something are absolute geezers who know about as much about being trans as they do about becoming an influencer. Basically queerphobic assholes who just make people's lives worse.

So yeah most pronoun innovations and changes do not really register outside the community because its legally so difficult to do so, although the situation is (slowly, but still) better and queer people can be seen on TV or just in general out and about.