There is just a JIRA Cloud integration. Unfortunately there might be some cost and legal issues that don't allow a company to switch from JIRA Server to JIRA Cloud.
It would be great to have a JIRA Server integration that works the same as the current JIRA Cloud integration.
In the documentation you argue with compatibility issues with the different JIRA versions. There is an Enterprise Release for JIRA that most production system use: https://confluence.atlassian.com/enterprise/atlassian-enterprise-releases-948227420.html
It would be OK, to just support these releases.