Seriously, I don't think a bunch of people on MN can settle it. There is a lot of confusion. As TellsEveryone says, a lot of people think Transwoman means 'trans identifying female' and the rest play on that. TBH very few people have given the whole subject much thought, why should they, beyond thinking: each to his own, live and let live.
There is also a lot of shyness about what you actually want to say, or feel you can say. Transpeople are understandably pissed off when other people are curious to know whether they are 'really' trans, whether they've had the surgery. Only a small proportion of transwomen have, though I suspect most people not on MN assume it's part of the definition.
For many women, the penis has been an offensive weapon and it's been used against them - and they want to know if you're carrying an offensive weapon even though it's rude to ask.
It's a horrible operation, and the commitment required is a fair guarantee of good faith. It's a pretty safe bet that anyone post-op will be welcomed in women's spaces.
By the same token, it's a horrible operation so no one should be expected to undergo it. So where does that leave the decent-but-nervous-and-intact transwomen versus the autogynophiles and utterly opportunistic predatory flakes? How can you possibly tell them apart?
You can't, and you can't tell them apart from post-op Ts either, which is why self ID is an utter betrayal of transwomen. As well as natal women.
I joked earlier about 'lady'. I'd like to suggest this description of performing feminine gender as distinct from 'woman', which should be is a biological term. I suggest it as a parallel to the distinction between gender and sex. Its value may have sunk among feminists but don't you think it still carries the air of distinction that many transwomen desire? Or maybe it's not for other people to pin labels on anyone.