Which xpac has the largest MSQ difficulty jump from the previous one?

Personally I experienced difficulty jumps in the MSQ when going into a new xpac, then again, I am new enough for any difficulty variance between MSQ fights to matter personally. That being said, no xpac is uniformly easy (or hard) nor are the difficulty jumps between xpacs uniformly high.

At this point in the MSQ (I cleared Malikah but have yet to run Mt. Gulg) I have to say that, personally, it's a tossup between HW and ShB that has the highest difficulty jumps in MSQ content difficulty (from ARR and SB respectively).

Maybe you have a different experience of MSQ difficulty increases from an xpac to the next because I acknowledged that such items are subjective.

Before they gave us a difficulty selection for solo duties I would've said Stormblood because some of the solo duties used to give some people pause and you had The Royal Menagerie which somehow seemed to have gotten progressively harder to clear the later in the expansion we were, analog to The Dancing Plague now.
Now that we have the option to play MSQ solo duties at a lower difficulty if need be I find it hard to single out a particular jump in MSQ difficulty from the previous expansion, partly because it's been way too long since I've leveled through the content to have a clear recollection of its perceived difficulty let alone how difficult the content is for players going through it now.
My personal impression of, say, Titan will always be colored by how things used to be years ago (when the server locations were different, had like 2-3 seconds of latency by default and made the fight harder than it should have been) but things have changed since then and players doing the fight now will naturally have a different impression (and then there's power creep shifting subjective difficulty further).

If I had to pick one now I'd probably say Shadowbringers because it's the newest and as such is the least affected by system changes and power creep.
All of this, though, is looking at the relative difficulty of the expansion's MSQ content as a whole.
If it's just the initial difficulty at the start of an expansion we're looking at I feel like all of them start off gentle enough, especially so if you go in with augmented tomestone gear from the previous expansion.

Its hard to say, because over the years, both announced nerfs, and stealth nerfs had changed the difficulty of content.
With the biggest change being to increasing player max level, and max item level in ARR dungeons.

HW was roughly equal to ARR in most ways. Patchs of ARR had some harder content (from what was normal) But by the time HW patches came out, most of the ARR nerfs were out. (HW patches were easier than ARR patches)
The only exception I could think of, is Ravauna. To me its easy, and isnt really complex, but if enough people watch netflix during it, the group will wipe.
But even ARR had 2 MSQ fights harder than it, and I personally dont think HW MSQ fights ever equal those 2. (Steps of faith being the only one to come close to hard)
But HW did increase the complexity and difficulty of DPS, so that sort of counts...
SB mostly felt like more of what we had, with the exception of the final boss being a normal boss now. (Nothing in the fight is actually hard. Just a cheap tidal wave if you dont know how it works)
People still mess up some basic mechanics, but you really cant consider them hard. (Such as "press Vril to win") But there is one primal fight that does have slightly more complex mechanics than normal. And she's in a different league than anything thats come out before. I dont consider her "hard" since you can just rez through it all, but shes the hardest content in the MSQ so far. The main dungeons got a tad bit harder as well, but only for trash mobs, and only for those not geared/trying to do normal DPS rotations, while pulling 2 groups or more.

So IMO SB barely inches ahead of HW/ARR so far.

ShB feels roughly on par with ARR/HW. The final fight requires more effort than ARR/HW, but slightly less effort than SB.
5.3 MSQ boss seems to be trouble for people who cant use more than 1 button for the QTE, so this sorta counts towards difficulty. But again, that still leaves SB slightly ahead.

In the end, we'll see with the last patches, but as easy as SB was, imo it was technically "harder" than HW, and ShB almost equals it (not surpasses it) and ARR was vastly harder originally. So much so, Id say it was probably the hardest of all the expansions before the constant nerfs. (But not specifically the MSQ, more so other quests/dungeons. I only made this comment to say its not quite fair to say HW was harder than ARR, when comparing it to the nerfed version, rather than the original version)

Generally MSQ difficulty has not changed at all I think - design of dungeons and what new fancy glow effect do dodge or stack up has though (and how many they throw at you).

The invincible protagonist fights in Stormblood were more downright frustrating (and essentially pointless as you were scripted not to win).