This is a problem which crops up from time to time. The solution is to go to the Finder and swap the icon in the Get Info window of the app.
You may need to 'Approve' some or all of the steps with an Administer's name and password.
Open your Applications folder and select Affinity Designer, hit Command + I to get the Get Info window. Do the same for any other file. Choose the icon in the top left of the any other file get info window (click on it) Copy it and then paste that icon onto the icon of Affinity Designer's Get Info window. Immediately delete the pasted Icon from the Affinity Designer get info window.
You should now have the correct Designer icon after deleting the any other file's icon. All the copy/paste is done in/to the Get Info windows.
