All Ariens YT1138 I"ve seen used Briggs and Stratton 11hp engines. By the description of your carb, it sounds like a Briggs carb for them also.
The carb may still be available new from Briggs and Stratton.
Repair kits, floats, etc most definitely are available from Briggs and Stratton, as well as many aftermarket sources. You"ll need the model, type and code numbers to be sure you get the correct parts. Although a good dealer can match thme up without problem.
Engine model, type and code numbers are usually stamped right above the head bolts and sparkplug on the flywheel cover, or they are on the top of that cover, on the flat surface near the flywheel opening. Some also had the numbers stamped on the side of the cover, usually the flat side, not the rounded part.
You may have to clean off some rust and dirt and use a bright flashlight to see the numbers well.