That's where it always gets tricky doesn't it?
Because the books are telling you that Tyr (for example) is a god. It's not a debate. It's right there in black and white. There's no real doubt in Forgotten Realms are gods or not. Now, you can ignore that, sure, and add doubt to the setting, but, as written, there isn't any doubt. These are gods. They're listed as gods, they are described as gods and nowhere in any of their material is there even a hint that this might not be true.
Then you move over to a different setting, like Eberron, where it's very specific that these beings might or might not be gods. It's in doubt. It's a totally different approach.
That's where it gets so sticky with these multiverse approaches. Because all these different gods aren't different versions, each unique to that universe, like an infinite number of Spider-men or Loki's, but, rather, each of these beings are supposed to be unique. There is only one Asmodeus and he appears in different settings. There is only one Correlon, even if the appearance and details might vary somewhat from setting to setting. That's supposed to be the same being.
D&D's approach to multiverse has a serious problem. Instead of each universe being unique, you have many universes with these beings that span across them - which means that you get all sorts of conflicting information about these beings. It's one of the reasons I have always disliked the Planescape model which D&D uses. There isn't one Demogorgon. There's a different Demogorgon in every universe that has an Abyss. If there's no Abyss in that setting? Then there's no Demogorgon.
D&D really needs to embrace a true multiverse system rather than this sort of pan-dimensional beings threaded through many different alternative realities.