I worked in Spain for a long time, so when my DC started it was in a Spanish school, where there was no uniform and they could have whatever bag they liked, provided they could fit their homework folder and school planner inside. On PE days most primary kids just come in sports clothes (tshirt/joggers/trainers) so no need to change for PE, and nobody ever really brings packed lunches - kids either go home or have school dinners - so they fortunately never had to deal with that either. So all we ever really had to deal with was instruments on music days (everyone learned the recorder so that could just get shoved in the backpack) and the daily "snack box" with a juice carton and fruit/biscuits to eat during morning break.
I lived in Madrid for most of that time, where most kids in the city centre either live close enough to their school to walk or travel there and back on public transport so most had the wheely backpacks. For the commute home their bag could be wheeled (because they could get heavy, esp for little kids) ... but then during the day they'd be hooked onto their desk (I added a pic of a typical Spanish school desk that kids use from primary, below) so kids could access everything easily to put homework books in/get homework.
At the school I worked at, and my DC attended from 1ºEP (so YrR), at the start of term they would get a school planner (like the ones most senior schools in the UK have) with their timetable (even from YrR they would have a specific timetable of subjects) so you knew when they had to wear PE stuff, or when they needed instruments etc and they could write their homework assignments. Also the planner was used for any general correspondence or notes home from the teacher (eg "Don't forget costumes for the school play tomorrow" or "Juan was being a little silly in class today and had to sit out of football :("). It was also used for parents to send a note to the teacher (eg Juan has a doctor's appt today. Please send him to the office at 3pm instead of to PE) they'd just write it in the planner, so much easier than keeping track of bits of paper! On the rare times there were papers (eg a party invite), there was a little pocket in the back of the planner the teacher would slip it into.
They would also get a plastic homework folder, any workbooks would go straight in their bags, but if they had worksheets/papers to complete they went into their homework folders. Those folders permanently lived in their backpacks, and were only taken out to put in/take out homework sheets so less chance of damage/loss.
I loved that system, so when we came back to the UK I felt inundated with paper and bags and stuff that DC had to take to school!