OP, she's really pushing boundaries here, and you're not even close friends. The only reason she's expecting this is because they've broken up, you've said it yourself!
If she gets a new partner, or gets back together with him, she'll drop you.
Why are you letting her dominate this precious time??
Will she be there for you post birth during recovery, offering support? Unlikely.
You need to get her to back off, and she's not going to volunteer to to it because taking all your time & energy is working for her.
I'll give you a warning - when you have a newborn screaming with hunger / colic / latching issues, you're healing from stitches or a section or whatever else will need to be your priority very very soon..... You will look back on this intrusion and regret ever letting her steal the last few restful weeks before the birth from you.
Take it from someone who knows!! (In my case, an overly busy body elderly neighbor who completely piss took after I tried to be a decent person and help them out with shopping and internet admin .. ended up run ragged and stressed out and forgot to put myself/our family first).
Please tell her bluntly to back off. "I need to rest & prepare for new arrival so turning off my phone for a bit. Hope all is well with you." - then block her or put her on mute or something for your sanity.