Well, given that your surgeon and other HCPs are treating your gender dysphoria, it's not surprising that they would refer to your neo-vagina as a vagina - it is their job and correct medical practice and good bedside manner to use words that will make you feel comfortable. That's the point of treatment.
But you speak of having two children, by which I take it you fathered two children prior to transition. So you must be pretty well acquainted with a female vagina and what it can do. It is not a mere hole excavated in your perineum to accommodate an inverted penis. It is a muscular structure, capable of contracting during orgasm, with the internal lobes of the clitoris wrapped around the sides of its opening. It connects, via the cervix, to the uterus, and is the passage through which a baby can be birthed. It is self lubricating, remarkably elastic and just an all-round extraordinary organ.
I sincerely hope that the operation was wholly successful and it has made you more at peace with yourself and more comfortable in your own body. But what you have is simply not the same as what I was born with.
I suspect we do have some common ground. I have known a number of transwomen over the years - all of them very nice, thoughtful people just getting on with their life. However, that doesn't mean I'm happy to support self ID - because of the many reasons outlined on this thread, including yours.
Another area of overlap might be where you talk about a distinction between yourself and drag queens and fetishistic cross dressers - and I would totally agree with you that there is a huge problem there. However, one of the problems you and I both face is that campaigning organisations like Stonewall want to gloss over this important difference and include fetishistic cross dressers - exactly the sort of people I don't want in the changing room with me - under the trans umbrella. So the question is, how do we draw up the legislation to exclude them, while not excluding you?
However, we do have some points of difference., for instance prisons (an issue which I hope neither of us will experience personally), where I feel there have to be circumstances where biology matters. A post-op transwoman imprisoned for tax evasion - I can see why people would make a case for her to be sent to a women's prison (though I'd favour some sort of third space). However, it's estimated that of the 100 or so prisoners currently in the male estate presenting as women, slightly over 50% are sex offenders. (The stats were collected partly using court records, and partly using the fact that there are some male prisons which only house sex offenders). It'll be a cold day in hell before I support a biologically male sex offender being moved to a women's prison.
Can I just point out that a lot of us find the entirely spurious analogy of "it's just like blacks in segregation America" deeply offensive, because you are addressing women, who are the oppressed class, not the oppressors. We need sex-segregated spaces not to set ourselves apart, but to protect ourselves. It isn't the same at all (and a number of black commentators made this point in the aftermath of the Rachel Dolzeal case, when endless column inches in the press were devoted to Dolzeal/Jenner: compare and contrast). I've heard the analogy here re. transwomen of asking whether they're entering women's spaces as a refugee from toxic masculinity or a colonist - you have to be very careful that we don't read you as a colonist, because, like it or not, you grew up with male privilege, and we can spot the lingering residue of that a mile off.