I heard that the kart I drive has a closed diff, so I'm not sure if slip angles matter.
And I did learn some load shifting from GT. I used load shift to initate drifts in GT.
Your kart almost certainly has a solid axle. It's not a closed diff, it's no diff at all.
Slip angle is about the angle the tyre is from the direction it's going, and is very important for how much grip you get from a tyre.
Watch this from about 15 minutes or so. (I had another video in mind but I can't find it, maybe it'll come to me later.)
See how when he lifts off, the nose tucks in? All good sports cars do that to some extent, and it's especially pronounced in mid and rear engined cars. GT doesn't really do it unless you tune specifically for it, with tunes that probably don't match real world numbers, and even then it's iffy whether you get the effect you're looking for.
Ditto when he stomps the throttle and gets understeer. If you're in a car without enough power to spin the wheels up, or you're just careful with your right foot, that's what happens. The back squats under the power and pushes you out of the corner.
This is really important, because it means that you can control how the car turns in the corner by using the accelerator, even when your steering wheel may not be responding. You can control how the grip is proportioned between front and rear tyres to get the most out of what you need at any given situation.
Maybe I'm braking into a corner, and someone dives down the outside of me. I now need to turn tighter to give room on the outside, but I was already at the limit of grip for the normal racing line I was planning on taking. I brake a little bit extra as I'm turning to keep the weight on the front wheels. This means the back has less grip than usual, and starts to come around.
I'm scrubbing more speed by going sideways and I'm pointing the car tighter around the corner which is exactly what I wanted, I've made room for the other guy. But my back end is sliding out and I'm going to lose it. If I countersteer, I'll go out wide again and hit the other guy who is still beside me. Instead I squeeze the throttle back on and trade some of that front grip I no longer need (I've already got my car pointing more or less where I want to go) for some rear grip. The back stops sliding, and I power out of the corner side by side with my opponent having kept both of us safe to keep racing.
Outside of a few cars, GT simulates this sort of behaviour only in very limited ways. If you commit to a corner at the limit of grip, you're pretty much stuck to your line whether you like it or not. You can't fluff around with getting a bit sideways mid corner to scrub some speed, or flooring it early to get extra drive because you're already done turning. Weight shift exists in GT, but it's very, very limited compared to what a real sports car will let you do.
Driving an MX5 in game is like driving a brick compared to my real MX5 on a track. It just doesn't have the mobility and friskiness that makes it such a good little sports car. That goes for a lot of the great sports cars in the game, and a lot of the race cars too.
This is bread and butter for racing drivers, it's what makes it a skill. If all it took was to memorise the best line around a track and follow it, anyone could do it. In reality, you have to have a great feel for exactly how your car is moving with regard to the road, and you have to finesse your inputs to gently guide the car into doing what you want. It's an incredible feeling when you start to get it, and it makes driving into something much more akin to a jazz performance. Yeah, there's structure to what you're doing but you're making it all up as you go along to create that one amazing lap.