I am running CC 2021. Fresh Uninstall/Reinstall to InDesign version 16.0.1 x64 on 12/2/2020. Fresh OS update to Windows Version 10.0.18363 Build 18363. I have associated .INDD files to other programs and reassociated them back to InDesign. IDML files and all other indesign icons display correctly. All of the other CC programs I run have their correct file icons. But the only way I can tell an .INDD file is an INDD file is from the white boxes hovering above them. This has been a problem since I originally upgraded to 16.0.0. I even tried using a registry cleaner to see if that would work (ccleaner) and it found no issues.
This is a mild annoyance, but one that, after having spent several hours over several days reading/trying/trying again to fix, I thought I would throw this back out to the community to see if anyone has new ideas or if Adobe still acknowledges that this is an issue with the product.