"It is already morning, we are going to school."

"собираться" means to plan/ to be going to do something. It is not about motion at all. And it requires a verb or an event to plan to go to.

Since "собираться" can also mean to pack up, "Мы собираемся в школу" means a completely different thing from what is suggested, i.e. either packing up your stuff before school, or making plans and arrangements to go there. Which are probably very similar.

"We are going (to do smth)" - "Мы собираемся (сделать что-то)". "We are going" where "are going" is Present Continuous, is translated as "идём".