as for how bending actually looks, my thought was that dinos primarily use their head and tails for major bending motions, as most dinos dont have long or flexible limbs that would do much good, at least compared to human limbs. each bending looks slightly different, as with their human forms.

earthbenders are the easiest to visualize to me, as mostly they just do a lot of stomping and head throwing. foot goes down, rock goes up.

airbenders mostly rely on appendages that are feathered, so flapping wings or slamming down a very feathered tail like a fan. i have no idea what a non-winged airbender would do. probably not be very good at airbending.

waterbending is kinda muddy honestly, in my head they're mostly ground based tail and head swingers. less flipping than an airbender, but more mobile than an earthbender. i feel like sokka would use his head a lot though. he's not a bender, so if he wants to get a concussion blugeoning a parasaurolophus, go ahead man.

also also, airbenders and waterbenders can absolutely propell themselves with bending. i mean i guess all of them could if you want, but it's super common in air and water. air dinos flying in dino forms that aren't *quite* built for sustained flight (aang is a microraptor, which is a gliding dino, and not actually able to fly, but with airbending, that doesnt matter!) and water dinos bending while swimming in order to torpedo themselves through the water.

and then firebending is mostly reliant on the tail and legs if possible, basically use the tail as a replacemnt for legs in human form. loooots of roundhouse kick stuff. with a tail. also i was thinking that maybe it's normal to be able to spit fireballs like a dragon? but it's still kinda hard, and something most people can only do in dino form. idk about that one, i just like the idea.

i drew a bit of concept art for this waaay back, but honestly im not all that well versed in how to draw movement, so i feel like the firebender there is the only really clear representation of my thoughts. here's that pic, and a link to the post.

in terms of visualizing the movement, there's this one video game project though called dinoSword by Jean Nguyen that actually really represents what im thinking, even if it's a bit flashy and fast for what i mean. either way, it's badass and might give a good point of reference. absolutely check out their work, here's a compilation of some of their animations

and here's a gif of another one of their animations which i will try so so hard to describe in the alt text

so yeah, all in all super badass! definitely faster and more deadly than what i have in mind, but the general idea about the potential movements and range of motion for these dinos is there

(also a side note, in terms of species for dino forms, my half baked idea is that it isn't really based on nation or bending style as it is geographical location. like, those are obviously linked, but the cause is the physical location. so you can find spinosaurus anywhere you find water, even though it is commonly believed to be a water tribe dino. there are swamp spinos, earth spinos, and yeah, even fire spinos. yes, there are conotations and societal consequences to a fire spino, regardless of how accurate those assumptions are. it got worse with the war

the msot common species for each nation are: mid to large raptors for the fire nation, spinos abd cold weather dinos for water tribes, large herbivores for the earth kingdom, and tiny tiny raptors or flight adjacent dinos for the air nomads. maybe also some lil herbivores, and they just dont get to fly in dino form.)

in terms of what the actual element looks like while moving, i imagine that dinos would have a rougher time with anything that has a huge amount of finesse to it. delicate movements or anything super precise might not be worth it to do in dino form, and most attacks would be more explosive than their human alternative. that whole thing katara did where she incased zuko in a ball of ice in the s1 finale? not happening as a spinosaurus. so while a dino form might give a boost in power, it isn't always practical at the time. not to mention it takes energy to transform, and sometimes it's best to save that for the fight itself.

the general feel of the movements is much more flexible and weirdly athletic than any actual dinosaur would ever be. but at the same time, i want to impose this idea that dino bending, while powerful, can be pretty clumsy, and each dino brings it own limitations. large dinos like sokka and katara are automatically slower, and in fights like the ones we see in atla, that really matters. small dinos like aang and toph also have to deal with how lightweight they are. their natural defenses are to run and hide, so they dont get much in terms of physical equipment the way a large carnivore or herbivore would. they're much more reliant on their bending to stay safe than say a big ol ankylosaurus, who's built like a tank.