Desktop-based issue trackers are out of favor. Since bug/issue tracking is by its very nature something normally done among a group of people using separate computers, it's a natural for a client-server implementation. And these days, there's rarely a compelling reason for writing a standalone client-server app when the web browser is already installed. Quite the opposite, since keeping client software installed and up-to-date is a drain on the corporate infrastructure.
Trac is a very popular tool for issue management. It's even available as a VM appliance, so you don't have to do a lot of complex setup work. Jira isn't open-source, although, like IntelliJ, they often make it available at no cost for people who are themselves working on open-source projects.
Jira itself is written in Java and uses a fair amount of open-source code internally (their free licenses are a way of returning the favor). Since it's closed-source, the only parts of the product that you actually can see source code for are the open-source inclusions. I forget what Trac is written in. It is open-source, however.
An IDE is no substitute for an Intelligent Developer.