When to start underwear?

We started working on potty training DS2 right around his 2nd birthday, primarily because he would routinely wake up dry in the morning then flood his diaper at breakfast time. Once he finally figured out peeing and pooping on the potty, he has really gotten it, but generally ends up wetting/soiling 1-2 diapers per day. Unfortunately, he does not have the coordination to use the potty without help, and he is too big for the little potties. He is less consistent at daycare; he will use the potty for some of his teachers, but not all of them. He will frequently hold it so he stays dry most of the day at daycare, even if he doesn't use the potty. We are so proud of him - and really, really excited to be close to the end of diapers for our family. We want to encourage him in every way, but realize it is early and there is no real reason to push. Does anyone have advice about when to transition to underwear? I'm sure he can do it at home, but not sure about daycare or when we are out and about. He is pretty happy in pull-ups for now.

I wanted to add -

DD PT'd at around the same age, but was more able to manage her clothing and fit the little potties well. She was not as aware of when she needed to go as DS2, but did well being taken on a regular schedule. We moved her to undies once she was consistent at home and daycare, and it was very motivating for her.

DS1 PT'd around 2 years 9 months. We saw few/no signs at home, but daycare said he was doing great and asked us to send him in undies. They were right, and he did fine.