Why can two 85mm lenses give different background blur, and what actually affects perspective “compression”?

noticeably different “compression” or background appearance

These are two different concepts, which makes it difficult to answer your question as written. I will instead try to clarify the terms you use and provide some general guidance around the topic.

The general topic you appear to be concerned with is a perception of depth. "Compression" applies to the relative size of elements composing a scene. A tele lens tends to make objects appear at a larger scale than you would expect, due to the small viewing angle (cropping has the same effect). The viewer underestimates their distance, so objects before or behind them change less in scale than expected for their distance from the subject. That is called "compression" of a scene. In contrast, wide angle lenses tend to let the viewer overestimate the distance from which a photograph has been taken; consequently the depth of the scene appears exaggerated.

An entirely different element is the amount of background blur and its visual quality, "bokeh". The amount of background blur, given equal focal width and equal framing (and thus distance from the subject), depends on the distance of the background (for best effect, large compared to the subject distance) and the aperture number. A large aperture (indicated by a small aperture number) delivers a larger amount of blur that is measurable in the diameter of "bokeh balls", the visuals of out-of-focus specular highlights.

A higher amount of blur makes for better background separation, "uncluttering" the image and highlighting the subject. At equal subject framing and aperture number, the depth of field for the subject is similar, but a wider lens produces a much more cluttered image since the far background shrinks a lot in comparison to the subject (due to decompression of wide lenses), and the blurring of it shrinks as well.

At equal distance, focal length and aperture number/size, the amount of background blur is identical. The quality of it, however, may still be different. As an idealisation, the unsharpness exhibits itself by turning points of light into evenly lit circles. That tends to be "good bokeh", but there are considerable variations. One is "nisen bokeh" where the bokeh circles have a comparatively bright border. The result is that line features in the background are not as much spread out but doubled, looking like camera shake.

If you have a mild case of "nisen bokeh", that tends to pronounce the outlines of non-flat subjects a bit before the background, making them stand out or pop a bit, at the cost of a somewhat less smooth background. And that is one thing that can make lenses of the same specs and used at the same distance, focal length, and aperture make a somewhat different depth impression in the photograph.

So there are a lot of variables playing into the impression of depth. If you try getting more acquainted with the actual concepts in play, maybe you can narrow down your question to better focus it on the aspect you are interested in.