I disagree with this. Less than a year ago, you pushed a head out of your vagina/ had major surgery to deliver the baby, either way your body grew, sustained and expelled a baby.
And now you're pretty much single handedly caring for that baby. I have no time for men who put sex above the needs of their family. If he were doing literally 50%, you might feel more inclined to sleep with him. But, exhausted at the end of a day with a baby is relentless.
Don't let him say things like, "oh but he settles so much better with you", of course he blumming does, because you're there, persisting, even through the shit time - I'll bet it's not always plain sailing.
I'm a bit concerned for you that this sounds an ultimatum: have sex more regularly with me or I'll not marry you / I'll break up with you.
The question he should be asking is "How can we be a better parenting team so you get some time to yourself?", or, "How can I support you better?", or even, "I've noticed we've not been having sex much, can we get together at the weekend and discuss why that might be - it's still important to me and I feel like it's slipping away. I love you".
It SHOULD NOT BE, "We're not having sex, I don't want this for the rest of my life, I won't marry you". Real AH vibes coming in here!
I would be sure you're finances/go it alone plan are water tight.
Is he any kind of intelligent- emotional or otherwise? Get him to read up about hormones post partum and how the pp period is actually 2 years.
Sorry you're dealing with it, going through the first year with the first child isn't always a walk in the park, I'm sorry he's treated you like this. I'm sending a huge hug and hope you can sit him down to educate him and hopefully garner more support - as you rightly deserve. ♡