Can't imagine exactly how you can use pocket screws without an ugly
factor. I guess you could use those shaved of plugs they sell but as
soon as I consider using those it's a red flag that they aren't right
for the joint.

Regardless, a door takes an amazing amount of stresses. I built a pine
screen door using dowles that as a piece of furniture would have lasted
forever. It deterioriated in about a year.

I would go with M&T myself. If you paint it well, you could make it out
of any material really. Poplar would be a good choice. Cheap, great to
work with, stays straight, yada yada. You might drench it with water
sealer first and caulk the glass seats well so you don't get intrusion.

Reuse the hardware seems OK to me. Again, silicon ondet the
hinges\screw holes to minimize water damage.