Our system has all day K. Has for years. They have "rest" time but not all rest. The teacher uses that time to do one-on-one with some of the students whether it be for testing or remedial work.
My county has all day K and they do have rest time in the afternoon. I did my student teaching in kindergarten in another county and they didn't have any kind of rest time except allowing them to lay their heads on the table for a few moments during snack time.
We've had full-day K for many years. The students have a 30 minute recess and 60 minute lunch, just like the rest of the school. About half of each break is for eating and the rest is outside. They don't have a rest time.
Our K is all day, and they do have rest time, for about an hour in the afternoon. Our schedule was: Circle, math, specials, recess, reading, centers, lunch, story/song, rest, sci/ss, centers, dismissal. Our district has relatively long school days (from 7:50 until 3:20) for students, so they need the rest time. I know some places school days are much shorter, and rest time may not be as important to build in.
Our district moved to all day K years ago. My old school did a "quiet time" from August-October and let students rest their heads on their desk for 20 minutes after lunch. My new school just runs K on the same schedule as 1-5 and doesn't have any rest/quiet time.
we do all day. 8:00-3:35. No rest time. 30 min lunch, 20 min recess. Its rush rush all day long to meet all our requirements and rigor and other ridiculousness.
We go all day from 9:15 - 4-15. Kids have a 45 mins a day for support classes, 30 mins for lunch and 45 mins a day for recess. Recess is15 mins in the morning and 30 mins in the afternoon. My daily schedule is jammed packed because of all of the mandates. (90 min reading, 75 min math, 30 min writing, RTI,) We try to squeeze in science ans social studies in at the end of the day. There is no rest time. It's extremly hard to keep students awake at the start of the year.
We are full day K from 7:45 - 3:00. We have a "brain break" where students can lay on mats. The time varies from 30ish minutes at the beginning of the year to 10 minutes maybe on a good day by the end of the year. Some days we don't even get to it. We do have 2 recess times. A morning break of 10-15 minutes and a 30 minute afternoon recess.
Instruction is from 745 until 240, but many of the students arrive at 645 and stay at the after school program until after 5. They are fed 3 meals a day and a snack on most days too. There is no rest time. Only 20 minutes recess and PE 2/ wk for 40 minutes. Sometimes students fall asleep in class, but for the most part they are super high energy. In fact the past few days they have been more excitable than usual, perhaps time for some relaxation exercises like yoga or meditation.