The fact that you bring up sex every fortnight is sexual pressure. For a woman who really really doesn't want to have sex, this is extremely unpleasant. She's told you she doesn't want to have sex. So you continuing to ask (push) is disrespectful. It likely also completely extinguishes whatever flicker of lust she might have. It's really counterproductive and is creating a tense coercive relationship that is not conducive to pleasant mutually enjoyable sex OR a loving relationship.
That is very likely also why she is not physically affectionate (hugs and kisses and saying complimentary things about you) - because you'll get horny and then she'll have to turn you down, which will build into another tense argument where she again has to state her boundaries.
You must accept what she has told you.
My H and I had a similar situation when I became perimenopausal. I had no libido and he started complaining and crying about how sex was important to him. It got to the point that I literally felt revolted - nauseous - at the thought of sex and didn't even want to touch him because then he'd start grabbing and looking hopeful. I got really fed up with this. Eventually I told him I never wanted sex again, not with him, not with anyone, and we should divorce if he could not accept this.
My H thought about it for a week and then came back and said he didn't want to lose me, that sex was only a small part of our the richness of our relationship, and he could do without it. But he did want me to kiss and hug him and to be able to cuddle with me. I said I wanted to do that but there should be no expectations of sex.
So we rolled along with that for a few years (about 5), and he repeatedly made it absolutely clear that he was happy with how things were. In the absence of the pressure and expectations and tension, I actually started feeling flickers of lust and noticing how handsome my H is and thinking how much I love him. And we're now back at it, not very often, but it's very enjoyable and who knows how it will develop from here.
OP, stop with the pressure and accept what your wife says. Maybe you should get individual counseling to deal with it and help find which of the options open to you is most palatable: divorce or acceptance of a life without sex in the context of a marriage with someone you like and love and where you feel loved and valued.
I don't advocate opening the marriage because enthusiastic consent is needed from your wife for that, otherwise you will open a hornet's nest that will likely lead to a lot of trouble and pain and tension and eventually an unamicable divorce. I also condemn cheating, not only because it's shitty to the spouse but because it will require you to lie and live an inauthentic life.