There is an incidence of a very clear paradox in DS9. A Bajoran poet and writer comes out of the wormhole, and the Bajoran start believing that he is the true Emissary. It also clears up a mystery on how he disappeared, and never finished his most famous work. However, it turns out that he isn't the real Emissary, and was just send to help Sisko understand his role better, and the Prophets return him to the past. Where he finishes his greatest work. Major Kira remembers that it was an unfinished work, but when she checks the historical data, she finds the work completed and that the poet didn't disappear.Trek has generally avoided outright paradoxes in its time travel. We don't know how they'll resolve this one.
In the end, we can speculate endless what would "logically" happen. CBS and Paramount seemed to go with the Prime Timeline still being around to tell new stories in it, even after the destruction of Hobus. Everything in the TV shows, including Discovery and Picard are supposed to be Prime Timeline. Of course, only until further notice. Retcons are always possible.