The first thing you do when doing a Dark Sun conversion is ignore the second edition (revised) of the setting. The one after the books that every reboot of this setting ignores, since it takes Dark Sun, puts giant forests and oceans in the setting, goes science-fantasy, kills all the major villains of the setting, doesn't replace them, and makes peace and democracy break out everywhere.
TSR ruined Dark Sun in the 2nd revised edition, dropped support, and then went bankrupt. Stick to the core book and the first five modules (for information and inspiration; the plots of these wreck the world), and ignore everything else. You can get the first two books in PoD hardcovers, and I recommend doing so. Also, ignore the 4E update since the lore has been changed, the Dragonborn has been added, and we are trying to stick to the OG material without later revisionism.
The Dark Sun Rule Book will be the core reference work we will use for flavor and to guide us.
Of course, you will need the core Level Up Advanced 5E game. This is a given, all three core books.
The MOAR Complete expansion hardcover is highly recommended, as it features crucial elements such as half-giants and the elemental priest archetype, integral to the Dark Sun setting. There are no gods in Dark Sun, so the only cleric classes available are elemental clerics. So, as a result, do not use aasimars or tieflings in Dark Sun games. There are no gods so the elemental lords are the only source of divine magic.
Eliminate all fae and mechanical heritages, too. Beast kin is up to you, though I can see gnolls, stone forged, or desert cats as valid options. You can play an OG campaign or a more expanded game with more backgrounds; it won't matter. Everyone is under the dragon kings' claws.
Paranormal Power is another excellent A5E book if your Dark Sun game uses psionics.
You will have most of the heritages for Dark Sun, and if you want your game to be more 4E, you can include the Dragonborn. Gnomes are not in the original setting, nor are Orcs - include these if you want since your "view" of Dark Sun will be 100% canon only, or go wild. Me? I can see a place for Orcs in the setting, so they are in. Dragonborn may be seen as servants of the Dragon Kings, so they may have an "evil" Heritage as soldiers and enforcers of the scaled lords. Of course, outcasts and betrayals are always possible.
The Thri-Kreen will be your only missing heritage. You can always use the A5E Homebrew and Hacking Guide to create a new heritage for them or replace the Tabaxi from MOAR with this insect race instead of cats. Dense fur becomes an exoskeleton; you get a fury, a roar, a run power, and claws - it works.
Arcane classes are either defilers or preservers, and defilers use the Defiler Magical Destruction Table on page 60 of the Dark Sun rulebook (note this also causes a pain condition to all living things in the radius, even allies, save needed to avoid and throw off, use the poisoned condition in LU).
The preservers in AD&D 2E advanced slower but did not defile the land when they used arcane magic. Preserver classes should level half as slow as defilers, so double all XP awards to defilers (the things you ash and kill give you XP). Be evil, destroy nature, and advance faster; this is the world. I could halve XP for preservers, but that would create a situation where the arcane caster preservers would lag behind the non-casters.
All arcane caster classes must pick a defiler or preserver role, even bards. The two sides hate each other, so watch out. They do not "get along," and you can't have them in the same party. This insistence on "all ancestry and class options must get along" in today's games is beyond dumb, and it eliminates any source of conflict in the world. Can you imagine a modern "Game of Thrones" RPG where the designers insist that every house faction and background must get along?
Defilers are literally killing the world for power.
I always thought preservers were a weak option that kept the game in the "status quo" and "keep players happy" land; preservers should require sacrifice to have power, and you don't get something for nothing. Preserver power is this sort of TSR symmetry BS they put in their games, and it needs to have a personal cost instead of being the "default-free" option.
I would be happy to eliminate preservers and have all arcane classes be defilers. This is how we played Dark Sun back in the day. If you want power, be a defiler or a priest of an elemental force. Or use psionics.
Without preservers, it is a much easier choice, and it heightens the need for scouts, material classes, and clerics. Psionics replaces the "good mage" and forces players into that unfamiliar power system.
But TSR says, "Don't stigmatize players who want to play Gandalf in Dark Sun!"
And we are stuck with free-magic preservers.
If the entire concept of your world is "arcane magic is destroying the world," stick to your guns and make it that way. Don't give players an easy out, or it invalidates the entire world.
There is very little metal, so iron and bronze items are rare and not seen in most places. Use the LU materials chart (page 322), especially bone, stone/obsidian, and wood weapons. Your weapons and armor will be breaking and need repair constantly.
I would stick with Level-Up spells, powers, classes, and everything else. The rules for survival and terrain encounters will be fundamental. Heritages are as you see them; they say many of the orc-type races were wiped out, but I could see them surviving. I would add a Naga heritage, desert lizardfolk, and others.
Steer clear of the metaplot! Do not kill the dragon kings early, like in the modules, books, and official timeline. You likely want "no place to run" and the characters living under an iron fist in the few spots of civilization left in the world. If they want to change that, they must take land, clear it, settle it, and avoid being crushed by the dragon kings. Either that or level up to a point where they can try to kill an immortal dragon. This is not a thing to do by level 5, but a campaign goal that changes the world, and you play in that changed world with the next set of characters.
Other than those notes, you should be good to go.
Oh, and never let up on the players. This isn't a "happy adventure town" where an adventurer class is allowed to do whatever they want. There are guards, and all of them are greedy and sadistic; they will confiscate your gear, make up charges, and lock you away to be thrown in the next gladiatorial arena. Corruption and grift are at an all-time high, people lie, promises are made and broken, and people fear the dragon king and the elite ruling class (and their sycophant wannabe friends). The parts of the city the rich live in are walled off, and everyone else, plus the characters, live in squalor. Thieves will steal from the characters constantly. Thugs will beat them up just for having a bad day. You will be stopped and questioned and likely taxed for spurious reasons every other street. Thugs will pretend to be guards and try to tax you. Sandstorms will sweep in and turn the roads into choking, orange, hot, sandblasting winds.
Your first goal may be to escape this hell.
And you will find out the wilds are no better.
You may have to establish a safehouse (that will likely not last long, or be a constant source of headaches), a secret camp out in the wilds (same), or join a criminal group for protection. You may sign on to caravans as guards, and that is a profession few survive long in. You will need survival and social skills, or you will end up stripped of your belongings and thrown in the gladiatorial fights again.
Dark Sun is very close to Cyberpunk in terms of dystopia and hopelessness. But there is no place to hide or social safety net.
To survive you will need to be worse than those trying to kill, steal, or use your life for cheap , bloody entertainment. You need to be harder than them all.
And when you are, you will begin to attract the attention of the true players. The rich, the servants of the dragon kings, and the high0level cartels. They have an endless need for enforcers and problem solvers, or problem creators. Getting more power is not a guarantee of safety, since notoriety can mean death, enslavement, or worse.
You may leave it all behind.
You may join them and stab them all in the back.
But there will be no where safe to go, ever, not in this dying world.