As a software developer, I use JIRA for companies and OpenProject (Community Edition) privately to manage all kinds of projects. But here are a few more suggestions that comes to my mind.
There are several project management tools specifically designed for organizing and managing music production projects or are flexible enough to be adapted for such purposes. Here are some open-source options you might consider:
1. Ardour: Although primarily a Digital Audio Workstation (DAW), Ardour also features capabilities for managing audio projects, which can be useful for organizing music productions. It doesn't directly support project management aspects like Jira or GitLab, but its strong audio management capability makes it a valuable tool for music producers.
2. LMMS (Linux MultiMedia Studio): LMMS is more of a DAW than a project management tool, but it can be used to organize music projects. It allows managing various tracks and samples within a project, which offers some form of management.
3. ProjectLibre: As an open-source alternative to Microsoft Project, ProjectLibre can be used for all kinds of projects, including music productions. It offers traditional project management features such as Gantt charts, resource management, and task tracking.
4. Taiga.io: Taiga is an open-source project management tool that offers flexibility in managing different kinds of projects. It could be adapted for organizing music production tasks, similar to Jira.
5. Redmine: This is another highly flexible open-source project management tool that can be configured for various projects including creative and technical projects. It features issue tracking, Gantt charts, and a wiki, which can be useful for organizing music productions.
While these tools may not all offer the specific features for music productions that a specialized music production tool would, they are adaptable and can be used to keep track of projects, tasks, and progress. It might also be worthwhile to use a combination of one of these project management tools and a dedicated DAW to cover all aspects of music production.