What fingerprint? We don't send device OS, IP address, geolocation... Impossible to do fingerprint from only a device UUID that does not means anything.
Device UUID will still leak an usage pattern. For example, if an UUID is active in the morning and in the evening during the week but at random times during the weekend you can infer that they are working, their approximate working hours and the fact they are not working on weekends.
Just a simple example - I’m sure a data scientist can do a lot more magic given enough data.
Usage patterns can be unique enough to track the same user across different services, some of which may have the user’s PII and thus a link to the user’s identity.
Could be a good idea to send events in batches, so the app collects event counters locally and only sends it in bulk every few days (exact interval being random). That way there’s no specific date/time associated to events, just that “for the past 3 days the app has been opened X times”.
Just a simple example - I’m sure a data scientist can do a lot more magic given enough data.