If a bug was addressed on the day it was created otherwise it takes around 24 times longer. It'll take one hour on the same day but after 2-3 weeks it will take more than a day to fix it and also recover the affected places.
In general, I can say priority is more align towards business value and severity is focus on impact of bug.
I'm using priority & Severity based assignment to bugs. To be honest, always bug fixing is not among favourite & preferred tasks.
If a bug is creating a value for the customer, it can be treated as any other PBI.
If that bug is part of the story, then it needs to be addressed within the same sprint, otherwise we contradict with the DoD.
In Scrum, being "bug free" is often one of the acceptance criteria or part of the Definition of Done.
That way bugs are tested for and addressed during the Sprint or are discovered during the Sprint Review and are put on the very next Sprint.
If a bug is discovered later, then it is put on the Prioritised Product Backlog and addressed in the appropriate Sprint based on how it hinders delivering value to the customer/end user.