Under advanced image trace, now when you use the dropdown palette and select 'Document library' and then select your own limited colour theme in the dropdown below, it makes no difference at all (even though it takes time re-rendering the image).

This used to work really effectively, but I've had these issues for some time.

I'm on the latest version of Illustartor 2020 (ver 24.2.3)

I've attached a screengrab so you can see the colours are not being used!