(perhaps the 3 provinces in the north east, but give it time, but maybe by then we life in some ultrafuturistic times, where everything is green and only every 30 kilometer there are spaceneedle (no reference to the thing with the same name) where all the people of that area live. So no infrastructure. Earth back to its untainted self and us locked up in ivory towers. With perhaps outings in some flying pods) hmm. Maybe I should write a book haha
If the other city has no significant industry of their own and only cornershops, little supermarkets and hairdressers and a bakery etc. Then yea if it is close enough I think you can consider it a suburb. But if it has factories offices and all the stuff the other big city has ( just slightly less) and is not connected. No I would not call it a suburb.
In the 2nd case when it ís connected, I still dont think it is called a suburb is it, it would an aglomeration or even conglomeration if I am not mistaken.
I think satellite-city is a better term to use. "Satellite cities differ from suburbs in that they have distinct employment bases, commutersheds, and cultural offerings from the central metropolis, as well as an independent municipal government"
Satellite cities are completely independent and self-sufficient.
(ps in many countries a suburb per definition can't be a city, only neighbourhoods. For cities that have become joined with another city and/or are dependent on it there are other terms)
If so I can understand your other choices.