Depth of Field – Does the amount of background blur change, given the focal length with equal framing?

Suppose I have two lenses, 50mm f / 1.8 and 85mm f / 1.8. I want to fill the
frame with the photographed object. Now, if the object is 50cm wide, I have
take the picture at a distance of 1,122 m or 1,888 m, respectively, on a
crop sensor Canon camera (crop factor 1.6x).

The depth of field is 3 cm, exactly the same with 50mm f / 1.8 and 85mm f / 1.8
lens.

Does the amount of blur in the background (that we can assume to be at
infinity) vary with the focal length?

I know that the depth of field does not vary according to the focal length, being only dependent
on the opening number. Or at least does not vary much: at 10 m, it's
2.74 m (objective 50 mm) and at 17 m distance, 2.71 m (objective 85 mm), with 10 m and
17 m giving an equivalent frame on these lenses. So, a very small variation can
to be seen with the focal length.

(Note: I originally used the term "bokeh quality", but apparently it meant something else, so I deleted it – what I meant, that's it. is quantity, not quality.)