Yes, daycare is definitely playing a role. My mum today picked him up after lunch (at 1.30 pm) and she drove to her house: he did not fall asleep in the car (sometime does, sometime not) and my mum says he was happily speaking during the way. Then she put him down at 2 and it took almost one hour for him to fall asleep!!!
And he was tired for sure, as it was up from well before 7 am (although he stayed in bed till 8, waiting for the sun).
Probably he was so OT and so exited for the EW and the morning at daycare that he couldn't really sleep. I think that his bad sleep is due to the excitement to be at the daycare, it should be much more tiring for him than to stay at home and he needs to get use to it.
So... what do I do now? Let him sleep till 4-4.30 (normally he sleeps 2-4) and give him the normal BT at 9, or let him catch up until 5 (he fell asleep at 3), if he sleeps, and going with a later BT at 9.30? Do you think that the last option would give the chance to reset him and bring him to his normal wu time at 8? Tomorrow is Friday so I can let him sleep longer in the morning.
P.S. I also think that in theory 45 min nap would work best, as it is more one sleep cycle. However, I never tried to wake him at this mark.