Ahh... ok. I'm not familiar with 5e cosmology. In 1e through 3e, extreme levels of adaptation were needed to survive on the elemental plane of fire.
Yep, I know AD&D the best. It looks like with 5e they've described the elemental planes as having a slightly different layout - much of the plane is a border zone that's more survivable for non-natives, and then the heart of the plane is the pure element that requires extreme adaptation to survive. I've been going with the 5e assumption (since that's what we're playing), but I think it can work for any edition.
For example, if you are using the AD&D/d20 Plane of Water, then Qaybar's planeshift into Water would look a little different... the Eternal Deluge around Sheikh Salib's place would expand to cover the whole city and just not stop until crossing into the Plane of Water. A sphere of air would surround Qaybar allowing its non-water breathing inhabitants to survive. This bubble, legends say, is a byproduct of a great spell cast by Jafar al-Samal, the first sha'ir, upon Qaybar when he hid his Seal there from other genie-kind.
But regardless, I suggest you work out in advance ahead of time how this is all going to work. For example, when they hit the elemental plain of water, are they going to be in a bubble of air, or is everything going to be underwater? When they get to the elemental plain of earth, are all the spaces suddenly going to be filled with solid rock, or is city going to snap neatly into a cave that fits it? If you don't have a bubble, then the city is absolutely going to be dominated by the need to be continually preparing for the next transition as the overwhelming factor in civic life. I have done basically zero world building along the lines of a city that is prepared for radical transitions in its environment.
Here's my conception of how the build-up to, and eventually crossing over into, each elemental plane would look...
Into Air: In the months prior to the planeshift, birds flock to the city in even greater numbers and fierce winds whip through the surrounding land, kicking up sandstorms (or tsunamis, or thunderstorms, or windstorms). Because the djinn are the most beneficent of genie-kind, many pilgrims journey to Qaybar in caravans the hunker down, pressing through biting storms. Sail-makers and skyship-wrights travel to the city to ply their trades. Sales of kites, winged mounts, and other magic trinkets allowing flying would skyrocket. Strange portents, voices, songs, and scents are carried on the morning breeze. Like our own world's Chinook winds, the city's inhabitants go through uncomfortable transitions, erratic behavior, and strange dreams. Eventually, after a particularly fierce storm, the city finds itself floating on an earthberg suspended on a roiling cloud.
Into Water: In the months prior to the planeshift, The Eternal Deluge surrounding Sheikh Salib's palace grows even stronger, causing roots to become inundated with water. Lotus blossoms bloom, but many land-based gardens begin to suffer rot, and the agriculture transitions to something more like fantastical hydroponics. The surrounding region of Qaybar's current plan gets hit by hard rains, causing rivers to flood, which is good for some crops like rice but bad for others as well as making travel exceedingly difficult. Boat-makers would begin to flock to Qaybar, working with great intensity, as would emissaries to the marids. Sales in magical trinkets allowing underwater breathing and aquatic mounts would increase. Rivers might shift their flow to fill in the "open mouth" of Qaybar's crescent. Eventually, after a hard rain on a cloudy/misty night, the city's inhabitants awaken to find themselves on a small island amidst an Endless Sea. Lower sections of the city - such as the "Charnel Quarter" - might become partially submerged, so, for example, the ghasts/ghouls serving Ibn Natn might become lacedons.
Into Earth: In the months prior to the planeshift, nightly tremors would cause rocks to upthrust around the city like fingers extending from the sands/seas/flames (or floating "earth-bergs" to be attracted to Qaybar as if by magnetism on the Plane of Air). These tremors might cause canyons to form, such that travelers to Qaybar must enter via canyon trails. Miners and cavers would be employed by the various nobles and merchants in great number, and mages able to cast
dig/
move earth/
passwall would be in great demand. Sales of lodestones, giant lizards, and magical light sources would increase. Strange creatures and secret passages may be unearthed in the "Charnel Quarter." Sandstorms / Dust storms would whip against the city's walls, and in the mind's eye might seem to momentarily outline a massive cavern. Nights would get darker and darker, with fewer and fewer stars visible. Eventually, after a particularly fierce earthquake / storm, the sun would not rise and the city would find itself either on the slope of a dark endless mountain or within a massive cavern.
Into Fire: In the months prior to the planeshift, temperatures would soar, the wadis (seasonal river beds) would run dry, and rainfall would become increasingly infrequent. Desperate travelers would seek succor from the jann, who can
create food & water as the surrounding region is plunged into drought and plagued by giant vultures. Remembering their suffering at the hands of the efreet, the jann of Qaybar would become increasingly militant and distrustful of those entering their city gates (are they spies for the efreet?). Mercenaries, armor & weapon smiths, and engineers would be commissioned for handsome fees. Mounts adapted to fire like nightmares would be especially prized, and sales of
potions of fire resistance (and similar magics) would increase. Hot springs would form throughout the city, with purportedly healing properties even as they wreck havoc on the agriculture. In the hot dry environment, different plants and animals would thrive. Dazzling light and blazing heat would increase to the point that outside of the city walls dry trees and bushes might spontaneously combust. Eventually, under the midday sun, the light would become blinding and the denizens would find that by night time they smoldering embers of the Plane of Fire surrounded their city...and soon the efreet would follow.
I'm also unsure that the Jann are well enough adapted to the other planes to live there without a bubble of some sort.
That's a difficult question to answer by-the-book, because originally jann in AD&D / d20 could survive on any of the Inner Planes for up to 48 hours, implying they could breath underwater...for a limited time. I'm inclined to think that if they can fly (like jann in AD&D / d20), then it follows they should be able to breath underwater just fine, being beings made up of multiple elements.
Yes, but I realized that I was getting all my world building completely wrong. I was building for a society that had been largely stable for centuries and had reached a decadent pinnacle. I wasn't building for a society that had a violent revolution 10 or 20 years prior, was in the process of rebuilding from that while facing the absolute certainty of having to defend itself to the last in a century. That society would look completely different, and almost all of my characters are wrong for it. The society that got out from under the throne of the Efreet a few years ago and was about to face another plunge would be 100% devoted to military affairs and could afford to be 100% devoted to military affairs. Unless you know that you can weather the coming storm, no one is going to relax and do anything else. Forget art and decoration, we need walls, siege engines, gates, weapons, armies, fortresses, and mighty spells and we need them now.
I don't know that my timeline is better, but I think Qaybar is a very different place if this is the first cycle that they've been free or if they know that in most cycles they become enslaved. Qaybar only looks like what you've been describing if Qaybar has gone through the trials of several cycles and been able to handle them. Some of my PC really can only be understood as being someone who remembers what it was like before Qaybar had relative peace, security, prosperity, and stability. The Qaybar early post revolution is dominated 100% by characters like Maysoon Lubadah Kanaan and Sheik Abdul Rayib Bey Salib. There are no other factions around really at that point. Everyone is basically either Fanatics or Extreme Fanatics, and everyone is going to be pretty much going, "They are going to want revenge, and we've only got 100 years to get ready." Your description of Qaybar places the armed forces as being only about 3% of the populace. In a situation of existential survival, I'd expect the armed forces to be closer to 8-10% of the populace. My assumption was that the first 3-5 cycles, the Efreet wanted revenge, but gradually as it became clear that retaking Qaybar was a costly enterprise with small reward, the Efreet finally rationalized to themselves that they didn't really want that wet, dirty, breezy city with its mongrel inhabitants scarcely fit to be slaves anyway.
You're right, I'd been working from an original inspiration with a short timeline... But really I was designing for an old stable society far-removed from the initial efreet subjugation. My conception of Qaybar, like you can see from my 3% of the populace being armed forces, was of something more complex and layered. More "cold war" with the efreet (pardon the pun), than outright warfare.
I like the idea that only the most diehard militants among the efreet still advocating taking the "mongrel city" of Qaybar by force, and without the collected will of their great nobles, such efforts do little more than inflict minor damage to the jann.
I do, however, envision a few efreet magic-users trying to crack the code of where the Seal of Jafar al-Samal lies, and so they act in Qaybar under disguise, through intermediaries, or through political subterfuge.