Slightly unfortunate for people who did story quests up to the antitower without improving their gear, yes, since that's the biggest item level gap (partially because 3.1 had no main story dungeon, antitower is 3.2 content). Still, Stormblood will undoubtedly have level 60 vendor gear that's 230+ just as Heavensward has level 50 vendor gear that's item level 115. And worst case scenario you can get item level 230 gear from poetic tomestones, which even you probably still have some since they're the level 50 currency right now.
Basically, there will be very little to no grinding required to reach the item levels for story content.