You could probably find a summary of the story though and not miss that much especially if you sit a couple of hours in the inn checking the various cutscenes and stuff. A large part of the MSQ is still "go talk to this fucker, now teleport somewhere and go talk to another fucker" and the vanilla MSQ especially is filled with stupid ass filler bear quests in the middle of the MSQ(HW MSQ a lot less so, still has you running around talking to people, but it's a lot more focused).
I think the main issue is the Stormblood storyline will spoil a bunch of the large changes in the previous MSQ. Not gonna go into it cause spoilers but there's A LOT of stuff, most of the good stuff too, that will be spoiled in the first 15-30mins of the Stormblood MSQ just because some NPC will reference to it in some way, so that part kinda sucks.
There's also the lack of content kinda? I mean Stormblood will take a while to finish if you're super casual about it, but once you're done nothing's left.
My advice at least would be, I believe they said there would be a potion for vanilla and a potion for both vanilla and HW. I'd consider just getting the vanilla one. The vanilla story is, for the most part, pretty forgettable. There's some good moments near the end that led to Heavensward, but watching the cutscenes is probably good enough, and a lot of the original 2.0 stuff is quite honestly pretty garbage(the dungeons and stuff are cool like the primals and castrum and what not, but you can still do that fine without the quests around it and not miss much imo). The HW story is pretty nice, isn't full of fillers and you wouldn't be far from Stormblood anyway. You also have access to all classes.
But if you skip everything that's fine too and understandable. Just probably won't feel as impactful to see the Stormblood story stuff without having seen the previous stuff, especially all the building up they've been doing in HW.