If I change and/or add a priority – can I do so only specific to an individual project – or will it be global across projects?
I'm sorry to say that "priority by project" is one of the oldest and most requested features that is still not done by JIRA. It was requested for version 2 over a decade ago, and still hasn't been looked at (apart from developers going, "ooh that's complex, can we do something else?"
So, no, Priorities are global.
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