It’s probably just as “locked” as any other time period, which is to say not at all. Recent SNW episodes have hammered home the idea that the present, past, and future are all somewhat malleable.

The existence of time travel and the idea of a Temporal Cold War suggests that any given future is just one of many possible futures. The events in Discovery are canon, insofar as they did happen, but whether future Star Trek properties will take the Discovery future as a given is a more open question. Discovery was written very deliberately to avoid being constrained by canon, but that also means that the events are narratively very removed from the rest of the franchise.

My guess is that whoever ends up in charge of making the next chapter of Star Trek will want to establish their own timeline going forward for the same reason that the Discovery creators did, and they’ll largely ignore the easily-ignorable Discovery events, at least as relates to the far future. The alternative is either to set the next series in an even more distant future, which comes with its own issues, or setting it before the 31st century and having to write around a whole bunch of barely-established future canon that only applies to Discovery. I could be wrong, but it seems like the path of least resistance.

It’s just a future, and can be changed. I’m not aware of any objective in-universe measure of what is and isn’t the prime timeline, it’s really just what the writers choose to depict as such, which events are altered by time travelers and which ones stand. Since we’ve seen a full two seasons in this version of the 32nd century, it’s more likely that future shows will try to keep consistent with it, but it’s also possible they’ll be “retconned” into an “alternate reality”.