I would treat it similar to BSG’s jump drive.
You need to be able to calculate the jump coordinates.
If you cannot do that with high accuracy , bad things might happen.
No such limitation.
When Stamets injected himself with the Tardigrade DNA, he knew where to go.
Forgive me if this has ever been mentioned in an episode (I'm pretty sure it hasn't), but does the spore-drive have a maximum range? Or is it literally capable of letting the ship wink out of existence above Earth, appear above Ocampa 70ish thousand light-years away in the Delta Quadrant, then vanish again and appear in the Omarion Nebula another 70ish thousand light-years away and so on? Or further still and you're in the Andromeda Galaxy in the blink of an eye?
There is no maximum range in the conventional sense... Discovery can go anywhere in the universe.
The only limitation is Stamets and how many jumps he can make in a row (and how many Spores Discovery has at its disoposal).
We've seen that doing 133 jumps one after the other put a HUGE amount of strain on Stamets (I think Discovery made about 50% of the jumps before Culber had to administer the drug to stabilize him)... but we also don't know whether the same limitation would apply anymore, because at the time it was all new to him and he WAS eventually able to handle it (what put him in a coma was jumping from the Prime universe to the Mirror universe) - and the crew was able to replenish those Spore canisters too.
So, there IS a limit to how many jumps Discovery can make in a row before they overload Stamets... but there is no limit on how far Discovery can jump.
So, I think Stamets can tolerate about 15 to 30 jumps in a row with relative ease... you start putting a strain on him after that.
If there is a moderate 'waiting time' in between jumps, then Stamets is fine - but there is no limit on the range... so yes, they can jump from Earth to Ocampa, from Ocampa to Omarion nebula, and so on. They could also jump from Earth to the Andromeda galaxy and back again if they wanted to.
Albeit, once Tilly and Stamets make the Dark Matter interface operational, then Discovery won't be limited to the number of jumps it can make in a row either.
They said they could go anywhere in the universe in season one. Season 2's future wormhole escape made little sense in that they could have jump jumped 100 galaxies over and Control would never ever find them.
But it's Discovery, so these things just happen.
Small problem with that.
Control would still be at large, and it could still end up destroying all life in the Galaxy, or it could eventually track down Discovery on its own.
Without any limitations in how much it can grow/learn, Control could easily make technical and scientific breakthroughs from the massive Federation database alone in a staggeringly short amount of time and probably learn to track Disco through the Mycelial network... worse yet, it could probably end up developing its own Spore Drive and follow it if it wanted to (again in a very short amount of time).
But the premise Control needed the Sphere Data was really baseless. Sure, it would be a shortcut to evolving, but it could easily do that itself in a short amount of time.
Also, its desire to destroy all organic life makes 0 sense.
The writers could have introduced a fatal flaw in Control's programming which ended up putting it on that path... but spontaneous desire to destroy organic life 'just because'? Seriously?
Come on, that's just lousy writing.
Even an AI in real life would have 0 need to kill humanity if it surpassed the need for us. Why bother? Just build yourself a vessel and leave to explore the universe.
Besides, what was Control's end scenario? Meaning, what was it planning to do after it wiped the galaxy (and say the Universe) of all sentient life?
Also, there was no need for Discovery to make the jump into 32nd century once Georgiou defeated Leland/Control...
If they were afraid that it may have backed itself up somewhere and laid dormant, then the threat would exist in the 32nd century still because it could just lie dormant like that until it decided to reactivate and work in secret throughout the centuries.