My first thought would be to ask your friend what would be acceptable. She might not mind your different standards, especially since you'll have literally just had a baby which makes it much more difficult. She might also have some suggestions given that she also has children.

Also, have you talked with her about what to expect as far as help with baby and your needs go?

You could combine nursing tank tops with cardigans that cover your chest, like this one.

You can also use a nursing poncho like this one or this one to add quite a bit of coverage over any shirt or a nice easy button-front dress or nightgown.

IDK what size you need, but would a dress like this with loose-cut sleeves potentially work? You definitely don't need a slip under those dresses and they're super cheap on sale.

If you're going to have your own room, you could wear whatever you're comfortable in on your own, and keep a modest robe like this or this to throw on top of it whenever you're out and about, especially trips to the bathroom and such?

If you want to go very high coverage, sunnahstyle sells a sleeveless, zippered abaya which you can cover with a cardigan or robe.

And if you have time (or want it for later!,) https://sewprettyfabric.com/shop/ makes maternity and nursing dresses along with cape dresses custom-to-order. You can specify the sleeve lengths and all proportions.