Thank you so much to the both of you!

I managed to get my icon updated, but I have noticed that the icon is updated only if desktop-file-install triggers a file with a different name, so in my case I had to rename the new icon with something different from the previous icon of the desktop file otherwise it's not updated.

So if I have 1.png and 2.png and I want to re-apply 1.png to my desktop file I must run the script applying 2.png first and then I can apply 1.png, if I just re-apply 1.png it doesn't work (ofc, unless I refresh the whole homescreen).

Well, it's kinda weird and convoluted, I don't really know why it happens and surely don't have enough knowledge to dig into this, that's been just some emprirical observations.