I'm only updating my homebrew campaign setting to 5e, having originally created it between 2e/3e (I was halfway done when 3e released). And I've updated/revised/reimagined it several times since.
Link for the interested.
Although, back when I was doing my
worldbuilding blog on the WotC community site (and the
compilation book) I half-designed a world as an example, taking into account more 5e-isms from the start. It didn't change my process that much, since so much of a setting is campaign agnostic.
5e is very D&D, so it doesn't take much extra thought. The main examples of 5e-isms are including the in-world roles of subraces and subclasses in the world, and trying to accommodate those additions to the game. Such as establishing who the various warlocks might ally with, where totem barbarians live, or the cultural differences between high elves and wood elves. Bardic colleges required some thought, as did accommodating options like the monk. You always have to answer how monks fit into the world. Clerical domains fit into that, as clerics require that extra bit of forethought and worldbuilding.
For my current world, I've accommodated a lot of that. I've been trying to explain where the various races hail from, and giving some classes a dash of flavour. I might eventually give each background a (short) paragraph of world-specific flavour as well. Explain what it means to be a soldier or priest or outlander in the world.
Plus some thought on how the classes are seen and viewed by the kingdoms and common folk. Are barbarians respected or feared? Are druids weird hippies or one of the checks and balances for the world?
When converting to 5e, most of my changes involved races. I initially changed all the eladrin in the setting to high elves (having originally been grey elves in 2e/3e). But with eladrin in the DMG I might slip in a few more references. I had downplayed the current place of gnomes in the setting, as they were not playable initially in 4e, so I'm returning gnomes to prominence somewhat. Dragonborn and tieflings are well established in the setting (as were genasi and warforged).
My setting is a bit savage and uncivilized in places, being a dash post-apocalyptic. So the idea of barbarous people being rare didn't make much sense: large safe cities and civilized lands are rare and lots of people live in small makeshift towns or nomadically. So I did some design to separate barbarians the class from barbarians the culture.
Plugging the setting itself, it's post-apocalyptic D&D. The world has become tidally locked: one side faces the sun, while the other always faces away.
MAP
It's been a few centuries since the everything went heck and civilization collapsed; nations have slowly expanded and taken over the habitable land where life can survive. The ruins of the Old Order are still all over the land leaving lots of ruins to explore. Monsters are everywhere, having taken over much of the land.
It's basically D&D blended with as many post-apocalyptic tropes as I could think of.