My kid just graduated from PreK at Tubman, so I can help with a few questions:
-We sent a pillow/blanket/stuffy in a bag for the week and they came home on Friday to be washed. I think one kid brought a nap mat thing (blanket/pillow all in one), but I think we were outliers with the pillow. IDK, I just can't see sleeping on a hard mat without one. They're stored in the cubbies. I think they use the same mat every day. We didn't have any lice issues in two years.
-The kids went to the bathroom before naptime.
-Handwashing is a big one, but they do teach this at school too.
-All school supplies are provided by the school, so no need to buy anything. If you want to donate to the classroom, the teachers usually have an Amazon wish list. (Just ask when you meet the teacher.) Stuff like craft supplies and tissues are usually welcome.

I'd focus a bit on learning to eat from a lunchbox. We assumed our kid would eat the school lunches, but he's picky and prefers we pack a lunch. So opening/closing the lunchbox and whatever containers.

And welcome to the school. It's a wonderful community, and the PreK teachers are great! There will be a welcome to the school event in late August, and you'll get to go in with your kid to see the school and meet the teachers. They also usually do a home visit, so you'll get one-on-one time to ask all your questions with the teacher too.

You'll hear more about the classrooms later on, but as you're on here now I can tell you that they've moved from a looped (PK3/PK4) classroom to all 3s or all 4s. This was a decision made based on research that showed it was best for the learning of the PK4 kids. We loved the looped classroom, so I'm a little bummed. But I know it will be better in some ways too! The teachers will still stay with the kids for both years (so the PK3 teachers will move up to PK4 next year, and the others will move down to PK3).

I would order a nap mat. Just search for one on Amazon.

My kid is a picky eater, so although there is food, I also needed a lunchbox and bento boxes.

You should get a supply request list from the teacher. You can get everything the day before school at target other than they usually want those thick pencils and I had trouble finding them in the real world (v online).

Our teachers won’t apply sunscreen and my kiddo is super fair and burns easily, so I also got roll on sunscreen and taught my kid how to self apply before lunch recess.

I would try to work on not wearing a pull up during nap this summer if at all possible. I think most DCPS preK will let you use a pull up if absolutely needed, but trying to work to not need it. Our PreK 3 teacher did wipe poop if needed - not sure if thats Universal. For the nap you can get a nap mat or just a blanket and they send it home every Friday to be washed. Start reading lots of books about going to school and maybe some daniel tiger episodes about going to school.

I think bathroom independence and dressing/shoes are the biggest. Also following instructions, waiting in line, taking turns, sitting still during circle time, etc. Don't send him with tie laces! And I'm not sure DCPS does pullups at naptime, though I'm sure you could work with the school and/or teacher on that. Same with wiping.

We did pre-K at a charter, but yes they had little cots for naptime and kept a blanket there. If there's a lice outbreak, they'll get it from close contact anyways, so I wouldn't worry about nap cot storage.

My son starts PK3 at Tubman in August. He's our oldest, and he's been home with a nanny, so it will be a big adjustment. We haven't received any outreach from the school yet, which makes sense, but I want to just check in on "life skills" that we can work on this summer that will be helpful for PK. Any input from other parents who have been there would be appreciated! He is fully potty trained already (whew) and is pretty good at washing his own hands. And he'll eat anything.

Things we're already working on:
-wiping (he's bad at this - will the teachers absolutely not help? Ew)
-coat on and off
-shoes on and off (I assume they take shoes off for nap?)
-pull up on and off (he definitely pees during his nap every day - will he have a chance to go to the bathroom before/after nap to put on a pull-up? I expect he'll be able to do the mechanics independently by then, but he will need the opportunity and probably a reminder)
-telling us about his day (did he nap/did he poop) independently before we confirm with the nanny (since we know we won't get that kind of feedback

Also - what's the deal with nap supplies - I've heard he gets a little mat. Then do we bring a pillow/blanket for him? How are those stored (I'm concerned about lice)?

Anything else I'm not thinking of?

We've got a fair amount of travel in August, so July is the best time for us to prep, and I don't think we'll hear from the school before then, so any wisdom will be helpful!