About St. Petersburg/Leningrad...
We don't have to take this as proof that the Soviet Union still existed in Trek's timeline past 1991, or even that the city's named reverted at some point to Leningrad, as in modern-day Russia, the oblast (federal district) is still called Leningrad
. We can just say that Chekov was referring to the Oblast. AFAIK the few other times Leningrad is referred to could also be taken to refer to the Oblast.
Furthermore, many people in Russia continue to refer to the city in casual conversation as Leningrad, in much the same way that many people in the former South Viet Nam still refer to their old country's capital as Saigon despite the name change to Ho Chi Minh City. We could just assume that this pattern will continue into the future.