Due to licensing and data security requirements, we are looking at Jira Software in a Server/Data Center deployment. My team only needs Jira Core functionality for project and task management and it looks like Next-gen aka Team-Managed projects would be the way to go for us. Is this supported outside of cloud deployments?
Team-managed/Next-gen projects are a Cloud only construct and are not going to make it to Server/DC.
They're partly based on a different architecture that DC probably won't ever support. I can't rule it out, I'm not an Atlassian, but I can't see them going to DC.