Although I don't understand the math part, pressing play in that file before/after the patch shows pretty clearly the benefit of orthogonalizing the matrix, since the Limit Rotation constraint with Limit XYZ all turned off should have no effect at all, and that is apparently not the case in current master. That part really just seems like a bugfix, so that gets a +1 from me.

For the new Order input in the constraint though, I tried coming up with a case where there is a difference between the different rotation modes, but couldn't:

And in the file attached in T83908, the rotation order always seems to be left as Default, so that doesn't show how it can be useful either.

Euler angles are meaningless without a rotation order, and the order does matter a lot. You need to use big angles on multiple axes to see the difference obviously. The reason for the option is explained in the description, and Copy Rotation already have an order option.

What is obvious to you is not obvious to me at all! I have admitted to you many times before and will a thousand times again if I have to, that I am just a fraud who clicks buttons and somehow gets rigs out of them without understanding literally the simplest piece of maths that's going on under the hood. You could put two 2x2 integer matrices in front of me and tell me to multiply them, and I would stare at you with hopeless dead eyes, not knowing how to do it without googling it first.

And I think patches will get into Blender a lot smoother if contributors assume that everyone is as dumb as I am, lol. In this case for example, if you hit me with an example of where it matters, me or a code reviewer don't have to spend time trying to figure it out by ourselves, if you can slap a blend file together in 2 minutes, even if it is something totally obvious.

This demo file of mine from 2 years ago demonstrates decomposing the same rotation into different euler orders. The one you see immediately after opening the file has two similar outputs and one very different; and in different orientations the similar and dissimilar groups change.

Euler angles is the same as 3 parent objects, each of which rotates only on one axis. Changing the order of parenting affects the end result.

While I think that file is really awesome at visualizing euler rotations, it only shows why result is supposed to be different in the case of Limit Rotation. And I actually thought I understood this part, until the moment when I actually changed the rotation order in the actual Limit Rotation constraint with the patch and I saw no difference, and I was actually surprised. This is why I'm asking for a file where changing the rotation order with the patch actually changes the result of the Limit Rotation constraint.

Sorry to keep asking for further and further clarification in not only this but other patches, but the usefulness of new features must be crystal clear, especially since this area of Blender is not that well known by most who are available to review patches (afaik).

Well, this file demonstrates empties animated in quaternion space and clamped with Limit Rotation using two different euler orders. The file requires a build with this patch applied.

Without the patch the order used by the constraint is locked to the one used by the animation channels, or only XYZ if quaternion.