I'm not much into BJJ and don't have much contact with those that do. I thought I'd see more in this thread of how BJJ people see their art. Do they see it as a TMA or its own category? and do they see it as a style of judo, or a unique style of its own? How do non-bjj people see it? And the reasons they hold that opinion.
I'm not deeply involved in BJJ myself. Done a bit here and there, but it's definitely not my bag. Like you, I want to make it clear that I'm not doubting its effectiveness. I just don't actually enjoy doing it. And I don't see the likelihood of my ever getting into a proper fight (on the ground or otherwise) as being high enough to warrant spending years on a thing I don't enjoy.
That said, I have spent a fair amount of time around BJJ exponents, and my general sense is that they definitely don't view it as TMA in the sense that term is generally used. Though, like Tony, I have my own reservations about the usefulness of the term. To me, TMA just connotes those styles with which the West first became familiar. Taekwondo is often regarded as TMA, for instance, despite being younger and no more replete with ritual and tradition than muay thai, for instance.
My feeling is that BJJ is generally regarded as its own thing. But I think this tendency to group things generally comes from a perceived need to associate them. And BJJ often does precisely what it sets out to do. It's like when people say that boxing is a martial art (as I do). People who go into boxing often don't say that because they don't feel a need to. They're boxers engaged in the practice of boxing. It doesn't need to be more than that. Martial artists sometimes make that argument, though, because we want that association with sparring, conditioning, and other desirable attributes of boxing. (To be clear, I don't think that's all performative. Borrowing from the training methodology of boxing to improve your martial arts is entirely valid.)
The BJJ practitioners I've called "friend" haven't even been in the habit of saying they practice "martial arts." They tend to say "I do jiujitsu." And that's an end to it (excepting those who train in MMA of course). BJJ has some of the trappings of a TMA, certainly. Belts, gi, etc. But even those aren't a given, when you consider the prevalence of no-gi training now. Then you think about the importance of competition in BJJ, which is far more optional in many TMAs.
They're all just labels at the end of the day, not all that reliable for conveying anything real about someone's practice. I certainly wouldn't be able to confidently characterise my own background in those terms. So it generally comes down to what a person or organisation WANTS to be associated with, ultimately.