It just occurred to me that, no, the 32nd century seen in Discovery might not be definitive. How come?
Take the 2009 Kelvin movies. If Captain Jonathan Archer time traveled into the late 23rd century then there's an equal chance that he would end up in either the Kelvin timeline or the Prime timeline. From his perspective, either of these are perfectly legitimate futures for him to be in. Him time traveling forward to the Kelvin timeline does not negate the existence of the Prime Timeline.
Using this precedent, we have no reason to believe that Discovery's 32nd century future is the one the Trek tv timeline as we know it has to go into, especially considering there's a full fledged time war in between Picard and Trek that warped the timeline over a gazillion times more than Nero ever could.
An understandable mistake, but no.
Your making the mistake of taking a single instant of time travel in isolation.
Take Sulu, in one universe he's straight, in another he's gay because of an event that occurred after he was born. How?
The incident that created the Kelvin Universe changed the future, but that means countless incidents time travel from Kirk & Guardian of Torromorrow, to Sisko and the Bell Riots, to Admiral Picard going back in time to protect Renee Picard, etc..., which changes what they did in the past, which changes the future.
So now events occur that change the hormone balance of Sulu's mom when she's pregnate with Sulu, changing him to gay in the Kelvin timeline.
A single act of time travel can trigger a domino effect that changes other incidents of time travel, which leads to changes to the past of the new timeline/universes.
So A (time travel incident) lead to B leads to C leads to D (which is time travel to before A) leads to pre A.