when talking about a specific place, use “in the” and when referring to the type of place in general, use “at a”

You can work "in" or "at" a school/hospital/bank. I don't know about U.K. English, but for the U.S., you must use an article with "hospital" and "bank". You cannot say "I work at hospital" or "I work at bank". "School", however, is different from the other two words. "School" is not just a place. It is an institution that transcends place. For example, when you say "Billy is in school" it refers to no particular place. Your "school years" are the years of your youth during which you are learning. This would be true even if you never entered a school building. You could, for instance, be home schooled, which means your parents teach you. If you ask a child "do you like school?", you could be asking him whether he enjoys his schooling, or also whether he enjoys his particular school.

You say at or in the x depending on what you do there or who you are there, and whether or not you work at x everyday or you work at x indirectly or provide a service to x. Actually this subject topic is very complex and there is not the space or means to give a one off simple single lesson in the Italki community questions area. I managed to find a concise answer for you. "Both 'at school' and 'in school' are correct and can be used, but their meanings are different. 'At school' refers to the physical state of the subject while 'in school' refers to the social status of the subject." copied directly from -> https://langeek.co/en/grammar/course/576/in-at-school

I work at school should be used instead of in the school