Long reply incoming, so will need to split this in two. Here's Part 1:
Your background surely is in aeronautical engineering? Or is this mostly pieced together internet knowledge on some aeronautics?
How much does the canards vs conventional layout mean for sustained turn in the context of J-20 and F-22? Seeing as canards are regarded by us non professionals here as having inferior STR compared to conventional layouts but often described as having superior supersonic kinematic performance. Could you explain a bit about the "superiority" in the supersonic regime? Does it suddenly get boosted in STR while conventional get nerfed here or does ITR mean more for some reason in supersonic? Is it simply a biological consideration given how a similar turn (tighter) produces greater Gs at higher speeds?
Angle of attack is mentioned a lot in the last few pages in the context of those two clips of J-20's turning at low speed. Just a more random question on this alpha, is it simply the angle between nose pointing and velocity vector? Or does it only apply to more linear/horizontal situations where velocity vector is perfectly horizontal (or as close to) and nose up with alpha being angle between these two lines?
No, I do have some engineering background (and if I couldn't say that a few years before I can now), but wrt to aerodynamics it's a lot of self study. It's not all pieced together internet knowledge either though. If you want to understand anything properly you have to tackle the subject seriously from a fundamentals up approach, actually have a sound foundation of the physics involved and not just recite facts and rules of thumb, ideally with a goal of being able to usefully reconstruct some practical effect or prediction from the knowledge. The knowledge needs to be functional. If you can't reconstruct what is likely going on physics wise mechanism by mechanism you don't really know what you're talking about. I was very fortunate to have grown up with quite a bit of technical education before diverging from that track in college, and also fortunate to have opportunities to close the loop after college too, to understand both a lot of the basic science, and also to acquire good principles for learning new subjects. It also helps me a lot now to have had hands on experience with the engineering, R&D, and product development process. That said I would never profess to have perfect or authoritative knowledge here. I only know enough to know what's probably BS and what's actually realistic or plausible, and to do some casual analysis for fun. So take what I say on these things as informed (to the best of my ability) opinion and understanding, not concrete facts of reality.
Wrt canard vs conventional layouts and how they compare on sustained turns, the framing itself is problematic. To put out an analogy, it’s like debating whether front wheel drive or rear wheel drive is better when comparing the handling and speed performance of two cars, or debating whether one boxer's left hook is better than another boxer's uppercut in a boxing debate. Neither tells you more than general characteristics or tendencies of the things you're trying to describe. It’s how you leverage those characteristics or tendencies that then translate to performance capabilities.
To break this down further, I think it's first necessary to understand that what your sustained turn rate is for a design is itself *not* a constant. For any given design a plane's kinematic attributes vary depending on flight conditions, and specifically altitude, speed, and angle of attacks, and the extent to which flight performance improves or worsens for each parameter (angle of attack btw refers to the pitch angle of the object of interest relative to the direction of airflow, or what is sometimes referred to as the "free stream"). At the most fundamental level what this means is that your lift coefficient and drag coefficient changes depending on altitude *and* speed *and* angle of attack, and the degree and trend of changes for each parameter is *different* and *independent* for each. In turn how those relationships between your lift and drag coefficients are defined depends the ways the free stream interacts with your plane's physical shape. Outside of some very general principles where we can derive some basic sense of what's going on aerodynamically, those relationships have to be determined experimentally if we really want to know them with enough precision to make meaningful relative comparisons.
Furthermore, different wings, fuselages, and other aerodynamically relevant shapes will typically bring different levels of gain or degradation to performance at different flight envelopes and conditions. I think getting to this point, it's typically useful to stop thinking about the attributes of the plane itself as conferring specific performance properties, and start to think about what's actually going on, which is how the physical shape(s) of the plane is interacting with the flow of air around it. In other words, what really matters here isn't so much "what does the plane have" but "what is the plane doing to the air around it". After all, the way planes work is that you're converting an opposing force from air pushing against your plane's movement and converting the force from that opposing flow of matter into a positive upward force rather than an opposite lateral force. And specifically, what's happening is that as the shape is pushing against the direction of mass flow pressure gradients will form around the shape, and if you can get the pressure gradients to be distributed in a way where one side of a shape has higher pressure than the other side then of course you will generate a positive force pushing in the direction from the higher pressure side toward the low pressure side.
If you think about it from that standpoint, what should then stand out pretty quickly is that well of course a complex shape is going to have different interactions with the flow of air when rotated to show a different cross section to the direction of flow. And of course the amount of pressure you can generate for each cross section is going to be different depending on the speed and density (and viscosity) of the air. And of course different shapes are going to create different cross sections at different rotations and will also interact with changes in speed and density of flow differently. And to further complicate the matter, the conjunction of different shapes and geometries aren't always additive in effect but often translate to those joined shapes being its own unique shape with its own unique interactive relations with the flow field, and once you add movable control devices and other aerodynamic features like strakes and LERXes etc etc, that picture gets even more complicated.
To illustrate this point with a concrete example think about how a high aspect ratio wide span wing. That kind of geometry tends to have very good lift to drag ratios at very low speeds, and thus have pretty good relative turn rates in low speed regimes. Why is that? Well think about what's going on with the shape of the wing in terms of its integration to the airflow around it. The wide span means you are essentially maximizing the amount of length that the flow of air is interacting with to convert the flow's opposing horizontal force into an upward vertical force. But this span wise exposure also means that as you go to higher speeds, keeping altitude the same, you're also increasing the amount of wing length that's exposed to drag, and air resistance goes up as a square of speed. And then the moment you start to hit the transsonic range, the compression shocks in the airflow also begin to interact with that whole wing span, causing drag to go up even more. How might you improve upon that situation? What if you reduced the aspect ratio (made the wing narrower), but tried to preserve the same surface area? Well, now you have a delta. You've traded away some positive lift generation at the low speed, but your drag profile is now much better at the high speed because the total span of the wing exposed to air resistance is a lot less. Meanwhile you've still preserved the same surface area so at least the amount of surface that your positive pressure gradient generating the lift is the same, even if the deeper wing itself probably also changes what the pressure gradient over the surface of your wing look like. Take this example, and think about what the lift coefficient curve in relation to speed, altitude (thickness of air), and angle of attack might look like for one shape vs another shape.