It’s a Briggs fixed-jet Pulsa Jet, not the 'far better' adjustable jet version (usually the kind with a slide choke) but it’s still good, just simplified. The Raptors used a special version of the latter but eliminated the choke and had other enhancements.
The filter you may want for that is the stock one which looks like a clamshell (a top and a bottom) affair or a Big Mac box. It uses a good quality flat “accordion” paper filter with steel mesh backing but personally I prefer an air filter assembly that doesn’t cover so much of the carburetor.
What you can do is use a PVC end cap as an air filter adapter, about 2 or 2.5” diameter and make sure the bottom is perfectly flat by sanding against a plate of glass or tile. Bore a large hole in the center (same diameter as the carb throat), and two holes for the mounting screws. Then you find an air filter that fits the OD of the cap...
Cut your own carb-to-filter gasket from a cereal box.