See, that’s why many women object to the term cis. It implies a subset of Woman. That’s also why many transwomen use it. Because they believe they are women
I have no objection to other women finding the term offensive, as I complete understand their objection to it. It's just not an objection I share because I've not personally encountered the use of the term 'cis' in any scenario where it wasn't being used to make it emphatically clear that the user was referring specifically to biological women and not including transwomen.
I suspect this is probably due to my line of work, where it's pretty much an accepted term because we have to quite often refer to groups using exclusionary language. I don't really have any thoughts on the 'transwomen are women' question so can't really answer that for you, all I can do is try to explain why I don't, personally, find it offensive even though I do understand why other do, pretty much for the reasons you've already outlined.
There’s a word that’s recognisable worldwide for biological males. It’s men
As above, if I was to refer to 'men' in my workplace, people would assume I'm including transmen in that, regardless of my own thoughts on whether or not TWAT/TMAM etc. This is exactly why 'cis' has no offensive connotations for me.
I can’t think of any situation where the context wouldn’t make it clear that the word ‘woman’ refers to sex
I encounter them constantly at work. It's one of the biggest issues when you spend a lot of time discussing other groups that you are not part of yourself, or have little commonality with. How to describe them, how to advocate for them, and unfortunately, how to 'label' them. As much as I dislike labels for a myriad of reasons, I do find that they are often necessary and do fulfil a purpose when it comes to clear communication.