办公室里的人都在忙于工作

These are very similar phrases,but they do not have the same connotation。Busy with somewhat implies that you are engaged in a constructive or fun activity:I'm busy with teachingI'm busy with raising childrenI'm busy with something my studiesI'm busy with putting this puzzle togetherBusy at somewhat implies a work or fight activityI'm busy at workI'm busy at fighting firesI'm busy at killing this video game monsterBusy with is also used to cover longer-term activities,where busy at implies an immediacy of action - something that needs taking care of right now。This is a quick answer - hope it helps!