In my experience (but maybe it's just me, maybe other people manage their projects differently), the type of task plays a greater role in its prioritization than the project. For example, we always fix bugs first, even if that pushes back delivery of new features. Stability issues are even more important than bugs. And security issues even more important than stability issues.

Yes you could have multiple boards, each with its own backlog ordered by priority, then use colours to see which tasks from which board are a higher priority. But surely the point of having an ordered list of tasks is to see which is the highest priority?