We can edit the issue type by Move option but to be frank it's not user friendly. Everyone shall consider that you can move the Issue from there but didn't get to move the issue type as well.
I think there should be in-line edit issue type setup too.
On clicking the Issue Type icon, user can see issue type list and can select whatever he/she wants the issue type to be.
Normally you can add the issue type to your edit screen.
Be aware that changing the issue type this way only works when moving to a type with the same configuration schemes. This means you can't move to a type with another workflow / screen scheme/ field configuration scheme
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