You can find a lot of information by googling "93/97 Shotgun". There will also be some suggested search terms that will give you additional sites to read.
According to Coyote Cap, the 93/97 is permitted at the Western 3 events. Also according to CC, the first guns evaluated were modified Model 97 shotguns that had larger than original openings in the top of the ejection port; so large that shells could be loaded from the top. That resulted in their exclusion from NCOWS events. IFAIK, the new IAC 93/97 guns that have the original slot size in the receiver top have not been re-evaluated by NCOWS.
My great grandfather bought a new 1893 Winchester when they first came out. It has a 30" cylinder choke barrel. It's still in the family and still works perfectly although it's not been shot in awhile. The '93 was chambered for 2 9/16" shells so modern 2 3/4" shells are too long for the chamber although many of the newer shells have passed through that '93. It's still in the family but sadly it isn't mine.
I see no reason that the reproduction 1893 shotguns with 1897 mechanics should be excluded from NCOWS events but I'm not the one making the decision.