I tought someone was going to sa that but Akaviri Potentate is from the empire when Akaviri had taken over cyrodiil empire for a time. They don't really match with the Akaviri armor.
The armor styles we have are Akaviri and Tsaesci and...sure Akaviri Potentate but not really as its a mix between Akaviri and the cyrodiil Imperials. But nothing about the mounts. I was hoping for a picture or something but it seems to be a mystery.

The racial mounts for each race? Well that's easy.
Welwa and Bears for the Orcs.
Altmer: Horses, gryphons, indriks
Imperials, Bretons are Horses.
Wolves, bears, Ram and Sabre cats by Nords
Camels, Horses for the Redguard.
Senche for Khajiit.
Nix-Oxes or Guars/Kagouti for Dunmer, alongside Dwemer constructs.
Guars or Lizard-Steed for Argonians
Bosmer its either Senches, wolves well anything connected to their forests really.

Akaviri...what would be their racial mount or to be close enough. Maybe snake like creature or lizard but since nobody been there, we don't know what creatures live there with the Akaviri. We know their culture is similar to Asians and Akavir is unexplored land in elderscrolls.

But so is Atmora (Nords ancestral home)
Aldmeris (all Mer's ancestral home except Maormer, Snow elves and Ayleid)
Pyandonea (ancestral home of the Maormer)
Yokuda (ancestral home of the Redguards)
Kamal (Unknown land to the North east of Tamriel)
Akavir is the half the size of Tamriel.

Atmora yes the lore says it to be uninhabitable due to it being to cold you freeze to death. However smugglers continues this tale/myth, but what if they are lying? They would have Atmora's coastal regions to themshelves and also Zenimax does not follow the Elderscrolls lore completely. Some things they have changed and like Dragons were only in Skyrim before but now there was even Dragons in Elsweyr. Its like they have the Eldersrcolls lore as base but they can go anywhere they want with the lore.

So maybe one day we can explore Atmora and meet ancient nords tribes and Half-giants like Lyris Titanborn. I mean also the Sea half-giants that we see in Skyrim has to come from somewhere as they arrived with boats when we explore western Skyrim.

Akavir, since its close to Black marsh and Morrowind maybe it has jungle and mountain regions. Also their culture may have become different when the Snake like creatures/people conquered them.

Well sure either an island or just parts of Akavir when we ever go there since Akavir is half the size of Tamriel. Just like in Tamriel not all of Tamriel is open for players to explore and may never be.

Edit: Hmm I found a text saying Tamriel invaded Akavir at least once...then there got to be something on what creatures lived there. Or...we just have to wait until the day ESO takes us to Akavir.

But there had to been humans on Akaviri. well first of all the armors that the blades use would not have fit them if it was not human made as they just reusing Akaviri armor and weapons. Also the design is human so. Also in Elsweyr when we play that chapter we meet descendants of Akaviri. I don't have in my head what they wer called. They lived for a time in cyrodiil until they decided to moved to Elsweyr. Imperials mingled with these Akaviri that got left behind from the first invasion as they could not kill them. and if they were not humans I doubt the Imperials still look human considering the Bretons are mix between elves and Nedic humans, then you The Reachmen which mixed by many different kinds of elves and humans and daedra yet kept their human look. As it says the Akaviri was attacked and conquered by vampiric snake people some time after the first invasion of tamriel...says that the Tscaesci was those vampric Snake people. And Ka Po’ Tun could not have had those armors that the blades uses as they are too big. And the Blades said they haven't recreated them, they are using ancient old akaviri armors and weapons they recovered from when the Akaviri invaded Tamriel.

Can't have been the Tang Mo neither as the Nords or Imperials never mentioned the Akaviri looked like monkeys. And if I remember correctly, the second invasion of Akaviri that took place...was it 100 or 1000 years after the first invasion. It was mentioned they looked like they had snake-like skin. If they looked like snakes and if the Imperial mingled with them then Imperials would not look human anymore.

"but my best guesses for the Tscaesci would be:
Horses, but a different species than Tamrielic horses" Hmm I don't think they had horses. Unless the mounts had shape of a Horse but was not really horses. Akaviri Potentate is the armor they used when Akaviri conquered and rule the Imperial city for a time and the Imperials got help from the Nords to drive out the Akaviri from the Imperial city and out of Tamriel. (Hence why the armor is mixed Imperial and Akaviri) But not all Akaviri managed to leave Tamriel and instead of killing the remaining Akaviri, the Imperials let them become part of the Empire. Hence the Akaviri "humans" from Elsweyr that wants to honor their ancestors as they are suppose to be Half Imperial/Half Akaviri.

https://i0.wp.com/eso.mmo-fashion.com/wp-content/uploads/sites/2/2020/12/Akaviri-Potentate-Male-Close-Side.jpg?w=225&h=722&ssl=1

https://i0.wp.com/eso.mmo-fashion.com/wp-content/uploads/sites/2/2014/04/Imperial-Galatite-Sword.png

Notice the armors have some similarities? Mix of Imperial and Akaviri designs.

https://i0.wp.com/eso.mmo-fashion.com/wp-content/uploads/sites/2/2020/12/Akaviri-Potentate-Male-Close-Front.jpg?w=344&h=722&ssl=1

"Some kind of land drake, like a dragon but smaller and not a dragon." Dragon you say...you mean like the Ornaug, they are kind of a dragon on land. I have two of them and they have scaly skin and fins. Would be cool if there was a version of the Ornaug had armor on them. That could be a Akaviri mount.

https://eso.mmo-fashion.com/wp-content/uploads/sites/2/2022/11/Amenos-Ornaug-Side.jpg