If you have the required access / permissions to your user id with which you login to JIRA of if you have the administrative rights on JIRA for your Organization, then the following should work.
Follow the API documentation here.
curl $BASE_URL/rest/plugins/1.0/
Usage:
curl -D- -u username:userpassword -X GET -H "Content-Type: application/json" https://<BASE_URL>/rest/plugins/1.0/
The command above will give you all plugins that are installed. You can then further filter on the list of plugins that are installed by users using the userInstalled
key, e.g. with jq:
curl $BASE_URL/rest/plugins/1.0/ | jq ".plugins | map(select(.userInstalled))"
Hope this helps!