Each one can give their definition since much of what we use of IT is terms coined by someone and adopted by the market means that without criterion, study or questioning. Some things are adopted in different ways according to the taste of who adopted from their understanding.
On Wikipedia we see some different definitions and if it is to check increases the confusion, each page says a thing. One of the pages talks about the possible etymology that would be window gadgets and I’ll stay with her. Then a widget is a ready-made software component that is related to some presentation control and/or user interaction used in a graphical window system. I see no reason to distinguish between desktop, mobile or web.
I see no reason to impose artificial boundaries on them beyond what was set out above so if we meet this criterion anything is valid. For me a button and some other components are widgets. Other Ides are like that too, some don’t even call these things widgets.
Google is known to release beta things as definitive and then how it was released gets complicated to fix. Google is one of those companies that say they are agile that value MVP and within this philosophy the important thing is to put something in the street and see what happens, to adapt. This never worked well, always generates products capengas or confusion for users, but there is a current that preaches that this is better than looking for excellence, good definition, something well thought out. This is for a case they didn’t think much of, they did. If they thought it was a better way to organize because it is well separated in the IDE, no matter if the definition is correct.
Deep down I don’t think it makes much difference where it is.