Usage 1: After doing ~ / Upon doing ~
Usage 2: For the purpose of ~ / In ~
The grammar structure 上で (うえで) has two main usages: expressing that something is done after completing a prior action, and expressing that something is important or necessary for the purpose of doing something.
When attached to a verb in the た-form, 上で indicates that one action is completed before proceeding to the next. It emphasizes that the first action is a necessary or deliberate prerequisite for the second. This usage is more formal than simply using 〜~てから.
The nuance here is that the first action is important and deliberate – not just a sequence of events. You wouldn't use 上で for casual sequences like "after eating breakfast, I went to school."
When attached to a verb in the dictionary (plain) form or to Noun + の, 上で expresses that something is important, necessary, or relevant in the context of or for the purpose of doing something.