Interestingly, I'd just seen a self-hosted, open-source JIRA (and Trello/Asana/etc.) alternative on Hacker News today: Focalboard. Looks pretty similar to JIRA if you're looking for a tool that's similar but free.
Another tool mentioned in that discussion was OpenProject for a bit of a more Todoist-style project management that could also work, though less similar to JIRA.
I'd used Tagia for a bit for a while back as a free, self-hosted project management tool. That one's far more different from JIRA but could be worth checking as well.
I've tried both Jira and Trello for project management. Then we switch to ZenTao. It fits what you want as being open source, on-premise, and jira like. Here is a list of 6 Best Free and Open Source Project Management Software (FOSS) in 2021.
Odds are your team doesn’t use the same tool to manage projects and assign work as you use to manage your personal life. Even your calendar appointments likely live on separate Google Calendars, on...
Particularly for comm tools like slack and zoom, and you are purchasing for a team, what admin features are most valuable to you beyond ‘standard’ user features?
We're a small team of 7 working in the event space and I've received a lot of requests about online / virtual events vendors. Would love to get feedback from other customers.