I'm with Old Mart here.
I think anything including the conventional 3 jaw may be misleading.
I've seen all your videos, but none show a clock gauge on the lathe spindle itself; obviously the step and face to the left of the spindle's thread provides a chuck register. Perhaps a measure there, and a gentle very thin application of Micrometer blue might provide a pointer.
Try it with everything you have that screws onto the spindle (except the Er32 chuck) and see if there is a common point of damage.
When you've satisfied yourself that the nose appears to be OK, start checking out your nice new collect chuck, and see what that and a bit of blue shows.
Introducing other items and then hanging the new chuck off them might be misleading, as there could be multiple compensating errors.
I'm not sure what procedure you were doing with the Arrand test bar, but I would have thought that would only, at this stage, prove the morse taper.
A possible thought, and a method I used when I bought a second hand 2 part chuck (of the RDG ER25 style)
The previous owner had failed to read any instructions, and rather than machining the dedicated mini-backplate to the chuck body, did it the other way around.
They machined the inside of the register on the chuck itself, but must have done so in an off-centre 3-jaw; It was a good 10-15 thou out.
In order to try and retrieve this, I mounted the ER chuck backwards, but without its backplate.
Essentially turn a length of bar to a good finish, held in your 3 jaw to a size suited to one of your larger ER32 collets, say 16mm. Don't adjust the chuck; now you know you have a bar concentric to the axis or rotation of your spindle, regardless damage or chuck offset.
Mount your new chuck backwards on this concentric stub, with the nut end facing the headstock.
Clock the register inside your new chuck.
Obviously don't re-machine yours, just clock it; in my case that was the whole idea in order to produce a new chuck register concentric with the ER taper, which I could then match by re-machining the backplate.
Bill
Edited By peak4 on 21/01/2021 18:11:15