No, the story content doesn't really get harder. Occasionally there are solo battles that are difficult when you're in minimum gear, but in fact if you spend poetic tomestones at the blue npcs at city state aetherytes, you can get the best gear for that expansion and destroy most of them. But there will be some exceptions.

It's not that they are hard either, but that sometimes it's not entirely obvious what it wants you to do at first, but after you figure it out, you know how that mechanic works for when they use it next time, because they re-use mechanics a lot through the game. Sometimes it just wants you to attack a certain enemy and you attacked a different one than the objective says.

Although these duties often have something that heals you, it is an advantage to take in a Paladin from level 58 because they have a lot of tank defense and can also heal themselves regularly with Clemency.

The story content with other players is regarded as easy by most players, but if for some reason it wasn't, they can beat the duty even while you're dead and they will resurrect you as many times as needed, so you won't have trouble with those.

The only very hard content in the game is labeled Extreme/The Minstrel's Ballad, Savage, Ultimate, criterion dungeons, the post-100 floors of Palace of the Dead or the post 30 floors of other deep dungeons. There are 2 or 3 relatively challenging Blue Mage fights in the Masked Carnivale. This is all optional (unlocked through blue sidequests), so it's easy to avoid if it's not your thing.

The duties around level 1-50 had a lot of changes recently to bring them in line with modern fight design. They used to be a lot more basic, untelegraphed and buggy-feeling, whereas the revamped ones feel a lot more polished and use mechanics they would use at level 90, and that is why you see so many new mechanics. You most likely noticed how some of the duties they didn't change feel compared to it.