I heard Bladewise (really good peach in WA; made Apex brackets) mention that, with Peach, never approach Puff unless there's a turnip between the two of you. This is true, Peach's that try to approach Puff without a turnip get easily out-prioritized and punished. With a turnip, she can move in rather safely or cover Puff's approach options around the turnip.
There's so much lag when picking up a turnip, they're not going to pull one if you're nearby. Especially given that they can't use most of their moves when holding one. When a Peach is standing there without a turnip, they likely want you to approach because they aren't planning to themselves. When they're spamming turnips, they're afraid of you so just be patient and find your way in. (Something like run up, shield turnip, shffl fair oos. Then you're close enough to apply pressure.) Just remember how limited peach is with her turnip, they're either going to float or throw it.
The trick is getting in on Peach, staying really close and zoning with bairs and whatnot. Peach is slow so you're trying to stop her mobility and apply pressure that she can't deal with. But, also make sure that you're playing very safe, Peach's loving fishing for nairs. It's usually good to distance yourself, but stay in that bair range and put hitboxes right by/above their head to scare them from floating. Remember that they can dash attack you safely while you're falling, if you expect a dash attack from them try to FF and shield-rest it, or just put out a hitbox right before you land.
One last thing to note: For some reason Peach's fsmash is really good in this MU. I still can't figure it out, but Bladewise uses it so much and it works so well. Like I said earlier, stay safe while zoning and expect golf-club range on every fsmash. Also, Peach can usmash you oos so don't fsmash or dash attack their shield.
And for all Peach's, fishing for utilt rest behind their shield is a good way to make them scared and get easy kills at low percents. After you have utilted their shield like this once or twice, you're often times better off mixing it up and getting the free shield grab. You have to mix up what you do in this MU.
Hope this helped.