The advantage of the Girandoni is that it had a magazine tube adjacent to the barrel. The newer ones don't.
Beeman's article. https://www.beemans.net/images/Austrian airguns.htm
A Girandoni receiver is more of a mill operation than lathe. The only part that needs turning is the threads for the air reservoir. Yes, a barrel has to be turned down and that needs a lathe. I'm thinking of taking CNC at Trinidad so I can make it from a billet. Trying to figure out what brass or bronze ally to use and I'm working on contacting a guy in Southern California who made one.
I would love to have a functional replica of a Giradoni, but as a collectable. Not a hunting rifle.
As for why they are not widely made today? Probably for the same reason that there are no Stagecoach dealers on the motor mile of car dealerships. They were replaced by more modern versions.
One of the things that strikes me is that the Giradoni and others of the type are "low pressure/high volume" airguns. A modern PCP uses a little squirt of air at around 3,500 psi while the Giradoni type operate at around 800psi mark, this is about on par with CO2 pressure on a cool day. Obviously this was about the practical limit for pressure in both pumping and storing the air - I'm just surprised it works so well.
Took the plans to the school and spoke with the CNC instructor during lunch. He said it could be done but would require the production of at least eight fixtures. If they had a four axis CNC, then probably only a couple. It would be easier to use a regular milling machine and hit things with a file…