If I recall correctly, it is indeterminable due to at least one cut between the ship jumping to warp and the arrival at the destination. No proof that plot duration matches screen duration.
There's no proof that plot duration doesn't match the exact screen time shown either. Jump Cut or Not.
They didn't have a title card showing <X amount of time Later>.
So I'm willing to take common sense at it's face value and assume things are in "Real Time" unless stated otherwise.
There is no "version 2," not in this sense. I mean "Timeless" indeed features a version adapted to Voyager and mixed with Borg tech, but QS always requires benamite, it was clearly introduced in order to explain why the crew could not just jump periodically, return to normal space before suffering hull damage and make repairs if necessary.
Benamite wasn't shown in the Arturis episode where QSS was first introduced, so the only thing I can conclude is that Benamite was used to enhance QSS V1 to move faster.
The fact that it's a rare mineral that naturally deteriorates, ergo makes it very rare is also interesting, but not a solution that Voyager can take care of when she has other priorities.
Don't forget Voyager already has a lack of man power & resources while trying to return to Earth.
So there's only so much time / resources for side projects or "Hail Mary" solutions like the Benamite Crystals.
1x time is enough for a "Hail Mary". Wait until you reach Earth / StarFleet and allow them to figure it out with more resources & scientific/engineering minds to help you.
If that had been an option, Voyager's officers and every damn warp scientist/ engineer in the Federation would be nothing less than IMBECILES.
It wouldn't be the first time, some Warp Scientist / Engineer in the UFP were IMBECILES.
Booker also confirms QS needs b. crystals in DSC.
The only thing he confirms is that his vessel's QSS drive needs Benamite.
We have a ton of (seemingly) contradicting FTL/ warp speeds already, even VOY (ep. 1x09) itself has a superfast warp drive "version 2" allowing them to complete the journey in about a week or less!
It's not the first "Super FTL Drive" of the week that fails to do it's job or only does a piss poor job.
Trek is litered with half baked & half cocked ideas that have severe flaws and are "Alpha Levels" of software development ready.
Do they just kinda forget about it?
No, but the crew of Voyager states that it would take "Years" to synthesize the Benamite crystal.
Given the wording, Minimum time of 2 years to make a tiny batch of Benamite Crystal.
Given the limited man power & main mission to get home, they had other priorities.
Especially with the crisis of the week they regularly encounter.
That's what StarFleet's greater Scientific R&D & Engineering Tech folks are for, after they return home.
They'll figure that stuff out once they get back & distribute the wealth of info that they've gathered.
To figure out how to mass produce Benamite, even if the realities is that it takes "Years" to do so.
We've managed to figure out how to make/grow things in mass on Earth, stuff that might take "Years" to do so.
I'm sure the UFP/StarFleet can create a automated WorkForce to do the same thing in due time.
QS speeds from "Hope and Fear" are already at odds with themselves.
- Dauntless covers >15 ly in ~30 seconds. - 1,800 ly per hour
Just like normal Warp Drive, you can tune up the engine to go MUCH faster, but you can't sustain it for very long.
1. Dialogue, same vessel: "In order to reach Earth [60k ly as stated in same ep.], you'd have to remain at slipstream velocities for a full three months" - 27.77 ly per hour
They must be running the QSS @ slower speeds, thats to conserve wear & tear on the StarShip frame.
2. Voyager with duplicated QS directly from Dauntless: "We remained in the quantum slipstream for an hour before it finally collapsed. Our diagnostics have concluded that we can't risk using this technology again. But we did manage to get three hundred light years closer to home." - 300 ly per hour
Not surprising, if you paid attention to when Voyager initially went into QSS & chased after the Dauntless, they were losing Structural Integrity Field strength just entering & from remaining in QSS.
Voyager literally lost 9% of their SIF strength just "Entering QSS".
Harry Kim states that they have < 1 hr before the hull of Voyager starts to buckle.
That means that any StarShip inside QSS feels crushing forces of some sort and it naturally will do damage/drain the SIF strength over time.
So no matter how long you try to stay inside the Quantum realm, normal matter can't stay in it forever, the natural forces will "SMOOSH" your vessel that you're in.
The best that you can do is bide some time & hope that the SIF lasts long enough to allow you to travel a significantly far distance at great speeds for that short amount of time you're in QSS.
No StarShip Captain in their right mind would risk their Hull Structure / Integrity if it isn't necessary, using QSS when it's not well developed / tested is asking for disaster.
Especially given how little they understood it at that time.
After Voyager returns, & the QSS tech is further tested / validated / better understood, newer ships can probably stay in QSS for longer periods of time.
Later vessels & along with the entire R&D / Engineering expertise from all of StarFleet might alleviate how much time you can stay in QSS, but it isn't indefinite.
The Quantum Realm that StarFleet discovered is something special, something that allows REALLY fast travel, even for a StarShip and all the stuff that it might carry with it.
3. Trek writers are notoriously incapable to adhere to consistency concerning FTL speeds since TOS.
True, but I won't hold it against them, they're mostly normal writers, they don't have enough technical staff on board to keep them consistent along with fact checking their math / work.
Most of the writing staff aren't tech / science nerds like us.
I think it is perfectly possible that the ship simply does not receive a 32nd-century warp drive upgrade. When Discovery gets converted in season 3, dilithium is still very scarce with no pathway drive in sight, and since its spore d. is their primary propulsion system anyway, they probably do not bother.
I highly doubt it, given the speeds we see them travel at, I think their Warp Drive is improved significantly.
By how much, that's TBD, but it's ALOT faster than what Discovery had when it started out.
See above, "slipstream v2" in terms of being faster is not a thing. If anything, it would be v4

, but in fact just another case of writers screwing up.
Given the "Hand Drawn" nature of the TNG era Warp Factor scale and how it rises to infinity past Warp 9.
And the extreme speeds that get discovered in the TNG era alone w/o Voyager's influence, it wouldn't surprise me that the upper limit of QSS V2 is 10,000 ly / minute.
But at those speeds, you don't need to stay in QSS for very long to cross the Diameter of the Milky Way Galaxy or cross the span between galaxies.
Speeds & travel time that seems practical once you have Benamite Crystals for QSS v2.
Even if it's a rare resource.
No. As per dialogue, even shuttles can achieve at least 0.7 c (209,854.72 km/s)
We rarely see vessels break 0.25c in most of the TNG era.
But that's what I think the 29th century "Hyper Impulse" is for.
It's to normalize Impulse speeds between 0.25c & < 1.0c
They have a way of getting vessels up to near the speed of light w/o having to suffer the effects of time dilation & not having to turn on the Warp Drive & all the energy drain that it entails.
They found a happy medium that allows them to go FASTER at sub-light speeds w/o having to drain ALOT of energy by using the Warp Engines to create a Static Warp Field.
TNG "Chain of Command II"
Acceleration is actually more important.
TNG and DS9 have also cases of FTL impulse.
But using your FTL engines to travel at impulse speeds (Sub-Light) seems incredibly energy inefficient & pointless.