It doesn't make sense to classify something for two centuries. Even the most secret operations are eventually released.
Have you met governments? There are top secret documentation stretching back decades, over incredibly minor things.
Given the implications of the spore drive and the like, I think that classification is appropriate for centuries.
The multiverse, the ability to bring back loved ones, as well as potentially multiverse destruction levels of potential. To name but a few. Yes, I would classify it for a few hundred years. And, keeping in mind, that in the future people live longer which means centuries don't mean quite the same as it does to us. Regardless, it gets filed, for me, under the phasing cloak, various time travel facets, guardian of Forever, Omega molecule and the like. Mentioned, serves the story, and filed away.
It’s in the same category as the Equinox aliens. Using it requires harming aliens. So Federation can’t morally use it, but if their enemies got it they sure would.
I wonder if there is a secret section 31 warehouse inside an asteroid full of all these things..... Wardened by Top Men, of course.....
As opposed too...what exactly? Starfleet doesn't use cloaking devices because they don't "sneak around" except when they totally do and have been researching one for years. Oh, and they use one in the face of bad guys. That Prime Directive thing? Totally a suggestion. I mean, Star Trek was based upon Westerns. It's the Wild West in Space!
I'm not going to do the multi-quote thing, but wanted to weigh in on TATV. I think there are plenty of worse episodes than "These Are the Voyages", but I understand ENT fans being upset that the episode was framed around two TNG characters and I can understand being upset over Trip being killed off and in the way he was. I can also understand those types of frustrations being multiplied in the context of 2005, because who knew when Star Trek would come back to TV? And the film series was dead. So this, as far as anyone knew, was it for a good, long while. People, understandably, would want the last Star Trek made for a while to be the Best Thing Ever and would be upset when it wasn't.
"The Wild West in Space!" Do you know how wild the "Wild West" really was? Sometimes it was a lot more wild than you think, but a lot of times it was lot tamer than you think. What was the armed force of the US government in the west that was most similar to the Federation's Starfleet? The US cavalry - or infantry, or artillery, as the case may be. Of course the most famous member of the US Army in the west was Custer, but only because of a famous disaster that happened to him. The most successful member of the US army in the west was General George Crook, who defeated more hostile Indians, and prevented more peaceful Indians from going hostile, than any other officer. He was an avid hunter in the wilderness and became an expert marksman, so that in various battles he shot at least 9 Indians. He might seem like the most "Wild West" of all army officers. But in his autobiography he told an interesting story. At the end of the Civil War, the Union army was being demobilized and the soldiers were eagerly and impatiently waiting to go home. The mustering out of many volunteer regiments was delayed due to improper record keeping and the men of those units were angry at their officers. And the officers of the 36th Ohio Volunteers, which had been commanded and trained by Crook, told him that the regiment mustered out without any trouble due to him teaching them how to do their paperwork. In Crook's words they thanked him for having "taught them their business". So the US army was already so bureaucratic even in the 19th century that even the most "Wild West" of officers considered an officer's business to be filling out forms correctly! The Wild West was in many ways a lot tamer than you think, and even the most "Wild West" aspects of the Federation and Starfleet are probably a lot tamer than you think.
I could imagine a centuries-long classification if some incredibly dangerous technology were discovered that could be replicated by any somewhat persistent group with access to relatively minor resources. Let's say the (crude) synthesis of Omega molecules, which is apparently not beyond the technical grasp of even pre-warp species- but the perfection (and safe storage) of it still eludes the Federation and even the Borg. It seems that by the time the Omega Directive takes place (the episode), the classification is over a hundred years old.
Greek fire. Secrets kept so long they're lost. Perhaps the best way to keep a secret, is too destroy all records. people holding knowledge in their heads age and die. Spore drive becomes a vague rumor.
Discovery doesn't need to still be classified for it to make sense that the 24th century shows never mentioned it. Only the spore drive needs to still be classified. Or, maybe it was deemed extremely important that nobody in the future know where and when Discovery was going to appear with the sphere data. The Federation was a century old, who knows if it's going to be around in a millennia? Who knows if they're giving all that data that almost destroyed them to some malicious force just sitting and waiting for it? A somewhat important question as well. What's stopping Discovery from just slingshotting around the sun?
The Federation still exists in the 29th century ("Relativity") so I'd say yes. Just another couple of centuries would be child's play to them.