So aside from Psionics, which are a given, the major things you need to do Dark Sun justice are:
1) Willingness to change the rules and ban existing stuff from the setting by default (obviously in a later chapter say "It's your world, you can ignore this, but..."). No existing 5E setting has really done this.
2) Half-Giants, Muls, and Thri-Kreen that don't suck. If you have to do something weird to make Half-Giants and Thri-kreen not suck, like make them a 1-level racial class (hello 3E!), then do it. Better that than Half-Giants which are Goliaths (ugh, I love both races but no...), or Thri-Kreen who are unexciting.
3) Preserving and Defiling being an actual choice, with actual consequences, and Defiling being being the default. As you can't use a massive difference in XP gain to differentiate them, you need to make it a serious choice some other way. But it has to be a serious choice. A big problem here is that Wizard in 5E is already a powerful, well-balanced class (this was not true in 2E, in 2E you were desperate to gain levels and escape from being bad and easily killed), so if you just make Wizards Preservers by default like 2E, you give no real reason to be a Defiler. Yet Defilers should be more common. So they're going to need a MASSIVE bonus. Like outrageous and unbalanced, in order to equal the massive difference in XP gain from 2E.
4) As per 1, ban most/all existing races, and any inappropriate subclass, including ALL current Cleric subclasses. Add Athasian variant races and subclasses as needed. All the Cleric subclasses should be Athas-specific.
Ban a bunch of spells too, anything that's inappropriate.
5) Equipment & Survival rules, and make them brutal. Weapons should break! People should nearly die of thirst! Nobody should be casting Goodberry!
6) L3 start + generous chargen.
We like tradition with other settings, right? So why do we not like it with Dark Sun? We should start people at L3 and give them a more generous character generation method.
If 5E couldn't handle this, I'd say don't do it. But it totally can! It can handle it with grace! And by all means encourage the DM to use more Hard and Deadly-class encounters!
And it will help give Dark Sun it's unique feel. Especially as you take away with the other hand with equipment.
7) Give everyone 1 Psi feat (as per the current UA) of their choice. Be clear that this is a one-off and doesn't mean your campaign is using Feats generally.