In RAM connection software, when I include axial load for double bent plate connection, it does not check for prying.
What design code are you using? I assume the plates are bolted to the beam and that prying is considered when the loads are only shear forces.
My question/comment is when you have both vertical shear and axial force on a skewed beam, the bent plate bolted (to the support column) - welded to the beam web ignores the axial force and does not check bolt tension & prying at the bent plate to column interface.
True, in the AISC bent plate (or double bent plate) connection template, only beam shear forces are considered. That's a limitation.