Does Pro have a tool or method to identify where a particular service is being consumed? For example, a single city limit service is used in 10 different web maps--how could I quickly identify which web maps (or other consumers) use this city limit service without having to open each map?
Pro itself does not. However, you can use the ArcGIS Python API in a Jupyter Notebook inside of Pro to gather lists of content items and identify which maps / apps they are part of.
If you are working with Enterprise, you have the option of using the functions dependent_to and dependent_upon to identify such items quickly and easily. If you're on AGOL, those functions don't work (yet), but you can iterate over a list of items and look for references to a particular item or service.