Have you tried, in the PDE, File > Preferences > Automatically associate .pde files with Processing?
I haven't, because I always run the PDE first, then open the sketches from there.
Plus, I have multiple versions, while the files would be associated to only one version.

" As mentioned, it did not work."
It wasn't clear the "option" was the one from Processing. There are lot of ways to do that.
For example, you can use the way Windows offers.
Or mess with the registry, if you know what you do (that's what I do usually, but it is more error prone for the uninitiated).

Perhaps you need to run Processing as administrator, before checking the option in the Preferences.