I'm aware of what some non-DL products have claimed, but the setting that the goddess exists in says otherwise.
From my perspective that doesn't matter. Clearly you believe otherwise. If the overgods (TSR and WotC) of the DL franchise say Tiamat and Takhisis are related and the lesser gods (individual writers I guess) say they aren't, whom should I believe. Typically I'm going with the overgods. It is ultimately their decision after all.
Are we going to pretend Eberron's
Tiamat is the same as well, despite being an overlord trapped underneath the planet rather a lesser goddess hanging out in Avernus?
It is all pretend, so yes I would say they are same. Personally I take the one god (or goddess) with many aspects /avatars approach. 2e Faith and Avatars suggested this as well (using Tiamat and Takhisis as an example, though the said you could have it either way).
Takhisis died, as in a final permanent death (not a copout like the Bloodstone Lands "death" of Tiamat). Cheapening that with the old "she was only an aspect" stretches credulity.
For you, but not for me (just the opposite for me actually). In fact, WotC is well within their right to say she never died in DL, that that story is not canon or whatever they want. Also, remember, it is all pretend.
FYI. I just want to clarify I was a big fan of DL when it came out, but I mostly liked original three, the Legend of Huma and Kaz the Minotaur. I didn't really care for the 2nd series even or never really read anything after that.
PS: I also want to be clear, that I am not trying to denigrate your viewpoint. It is completely valid. As are the one's I referenced. We make the game ours, and we we do so we accept, reject, and modify things as we see fit. That is the correct way to do it!