I can't agree with you:

Saying she's a lesbian because she enjoys sex with a man although not being attracted to the man or men altogether is similar to telling a trans woman she's a man because she has a penis or an X and Y chromosome or whatever.

I think it's wrong to use your criteria to determine if someone identified themselves "correctly" or not and we should be more supportive to the labels people feel fitting for themselves.

Your chicken sandwich example obviously is a hyperbole that doesn't help this discussion. Practically nobody would honestly identify as a chicken sandwich but there's a valid point in saying "I feel attracted to women and although I can get off by having sex with a man I identify as lesbian" as well as saying "I am a man feeling attracted to women, identifying as heterosexual and still I think a blowjob by a man would get me off"...

If you say you are bi then I would assume you will fall in love and be attracted to men and women not just have mechanical sex with men like it is a flesh dildo. So op would lie if she said she were bi. It would deceive men into thinking they had a chance and that she would be horny for them and fall for them.

She said she only falls for women, feel sexual attracted to women and if she could she would be with a woman. But she is fine with using her partner who she was forced to marry (sorry for this wording op) as a sex toy.

So I would call her a closet lesbian that is pragmatic.

Nonsense, your definitions of these trait label categories is entirely black and white, when in reality close to no one fits 100% into a category completely