JIRA certainly doesn't attempt to track read activity. That could potentially cripple it with load in any system with a lot of users. Write activity is mostly the point of JIRA though, but because it's interested in issue tracking, not what people are doing, the records of writes are scattered, and they're mostly about changes to issues, so not everything is tracked. Admin activity isn't tracked unless you turn on admin audits, and again, that's not 100% complete.
The best you can really do here is forget the application and read the access logs. Easy to capture that if you've got a web-server in front of it (like Apache or nginx), and you can enable it in Tomcat I think
As there is no built-in audit trail feature in JIRA, this comes down to a classical log processing problem:
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