I have been very happy with the two I have from Thirteen50. I have had them for 7 years and they are basically brand new minus a bit of a patina.

https://www.thirteen50leather.com/collections/full-grain-everyday-belts

Plaster over blue board is still common in the northeast. Everywhere else uses drywall. Not sure why.

If they are single glazed doors from before 1940 then it is easy to remove a panel of the glass. After that doors became much less servicable.

Drill it with a small regular drill bit first to line it up.

That said, I would much rather go through the wall with a pass through box of some sort than go through a door!

I did the same but through the wall. I would do it in the wall instead of the door. It will be better long term.