Puff is not limited to just rest and bair...
She has other tools.
I play the puff matchup a lot and have a decent amount of experience against players like 4%, and I think the mu is really good for ICs.
I was talking to 4% about it awhile ago, and we both kind of agreed that puff's best bet is trying to time ICs out. She has a lot of trouble getting in on them, and while ICs have to be more patient with their approaches, they can actually get through puff's defense pretty well if they are paying attention to what she's doing and don't get greedy.
I like to play pretty noncommital and just poke at puff a lot with uairs and wd OoS ftilts. And when I have a lead I just use a lot of blizzards to keep puff wary of my space. Blizzard outranges everything puff has, so good blizzard placement is really difficult for her. Just be aware of where she is when blizzard cools down.
I also have no problem timing people out these days if I need to, and I can give you some tips for that if that is your goal, but I generally don't need to against puff.
Big things:
1. Don't jab puff. A lot of ICs try to do jab->grab waaay too much. CC rest and SDI up/In->rest (if you jab her in the air) kind of destroy that.
2. Grab less. I don't try to get a grab unless I know I got it. grabs are huge punishes, even with sopo and/or without wobbling, but going for grabs isn't great in matchups where you want to try and not commit to anything unless it's guaranteed.
3. (2.5) be careful with blizzard->grab. It shouldn't ever really work on puff. I usually blizzard fsmash or usmash depending on how puff DIs. Sometimes you get bigger punishes off bair/nair/fair too though, so play around with that. Depending on how blizzards hitboxes come out (they are random), you can get away with blizzard->fair meteor->reset with last hit of blizzard sometimes, but it's really random, so I wouldn't really try to go for it too often. Puff can meteor cancel rest your fair meteor too, but it almost never happens (yet).
4. wd OoS ftilt covers puff's entire fade back before she can do anything else. If she starts doing higher aerials and jumping up you can uair or u/fsmash her.
5. a lot of puff players will do aerial->fade back->fsmash to try and punish you for wd oos or trying to grab. It's really bad if you're ready for it. ftilt hits her before she can even fsmash, but if you try to wd->grab too much she starts doing it. usually I do short wd->hold shield+shield DI in to just bait it out and grab it.
6. dair->rest is guaranteed on nana. You can SDI out of it, but nana is usually dead. I usually let puff take it and get ready to punish her missed rest. charged usmash usually kills at about 60%. at lower percents there are other combos you can do to maximize your damage output a bit. I like a couple like falling iceblock hammer->fair sweetspot or fair->dsmash or dthrow->nair->dash attack or some other weird ones you can do if you react to DI. It's fun to play with. Its ok to let nana die sometimes because sopo still does fine in the mu, you just can't wobble puff.
there was some other stuff I was gonna mention too, but I forgot it. I'll post more if I remember more.