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.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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