Don't make me break out the spacetime diagram, young man. Because I WILL break out the spacetime diagram.
Anyway, doesn't matter. Star Trek has messed with time travel since TOS season 1. And that was after they started introducing magic men with god powers, which they did in episode 3. It makes zero sense to get nerdy about it. That's my point here.
I love it when sci-fi teaches us about real stuff. The problem is that when you mix instant and classical (non-instant) communication channels, you get situations where information time-travels, and the receiver gets information from the future. This breaks causality (present based on future events), and so nature rightfully abhors it.
The closest we've come to instant communication is the use of entangled particles, but we can't make practical use of the phenomenon. Touch one such particle, and it's pair instantly changes to the opposite state. The catch is that you can't know when to observe the particle, nor can you know what the original state was, via the same mechanism. So you still need to use normal photons moving at slow-ass light-speed to communicate that meta-information, thereby undoing any attempt to exploit it.
Bonus points for starting with the point that forget warp, subspace communication breaks causality already, so you don't even need to boldly go anywhere for any of it to be kinda busted.
If that's a bit too dry you can search for a similar subject line, there are TONS of explanations like this one out there.
Anyway, none of it makes sense, it's all for funsies anyway. Suspend disbelief, ye nerds, and enjoy your sci-fi.
I think MudMan is correctly pointing out that to travel any slower than light speed through space causes time dilation since space is actually space-time.
There is a trade-off between how fast you travel proportional to the speed of light and how much time a stationary observer percieves to have passed compared to you who is travelling.
When you travel faster than the speed of light, all time and causality breaks down. This is not the case with how the writers of Star Trek wrote warp drive mechanics, this is our best understanding of the actual universe. Einsteins theory of relativity.
Fun fact: Light itself (or its quantized unit: the photon) travels at the speed of light and therefore experiences no time. If a photon is emitted from a star across the universe and travels millions of light years before eventually being absorbed by your eye, from our stationary reference point, the light has been travelling for millions of years, but for the photon it was instantaneous. Zero time passed for the photon. This is the idea of time dilation.
Yes, that's what I'm referring to. And a least as far as I remember, it does. It's not obvious and not addressed at all, but instantaneous travel between two points in space (if you don't take a shorcut through an addtional dimension, e.g. something we could call w if the three space dimension we're familiar with are x,y,z) is equivalent to time travel. The same is true for FTL travel, which Star Trek solves by warping space time, which also works.
Perhaps the mycelial network is basically an extra space-time dimension, but at least the way I remember it being explained that wasn't really the case.
But that's anyway a relatively technical points and Star Trek, as much as I love it, was never really about the technical things.