I doubt you will have any success trying to fix these as they are pressed and vacuum formed.
Look around for some second hand ones from a wreckers.

 

I experience the same issue, though not so big area. I assume it’s just the beginning (will spread) and it happened after or during the last summer.
Once I repaired such an issue on my old Skoda Fabia but it was the carpet on the roof from the inside (ceiling). I just guess there is a glue which after few years of service says goodbye and the any glued fabric or leather goes away like you showed (if not sewed but glued only).

There might be online shops to buy a meter of fabric or leather and definitely there are spray-glues for that to attach the fabric onto the plastic/metal surfaces (I did it once as i mentioned).
What is tricky, is how to make it nice on bumpy surfaces like that door handle and the area around. Of course, firstly that handle needs to be disassembled and cleaned. Pretty dirty job if there was some glue before, but the area is small, so maybe some 2hrs job I guess. But if you can find another spare part, might be a better option.

 

I think that we all have (or sooner or later will have) this issue. At list in the sun-kissed country where I live all Kugas are like that; I have seen at least 2-3 more cars besides mine. Please note that my car has rear tinted glasses (with foils) plus sunshades, but apparently these measures were not sufficient.

Strange thing is that it only affects the rear door panels but not the front.

 

The front and rear door panels are probably made in different factories, they could have used a different glue in the factory making the rear panels, and that has failed over time.