What could be a reason for this and where it can be enabled for editing again?
The interesting fact is that I can edit the same page properties in page -> page information -> edit template -> page information -> initial page properties This tells me that there might be some restriction in product-page template, but it has the same properties as content-page template.
I am logged in as administrator, so there should be no permission problems.
The properties are disabled because of inheritance. All properties are inherited from the blueprint/master. If you want to edit the properties you can click on the cancel inheritance button as shown below: