Where can I get a carburetor for a Snapper 41AR2HBC707 S27BV

Are you sure is isn't 2046, rather than 2446?

Support here

https://www.snapper.com/na/en_us/support.html

But, you need Engine Support, not Snapper Support. This is an oddity with small garden appliances.

https://www.google.com/search?q=snapper+st2446-00+parts+schematic

Carburetor info

https://www.google.com/search?q=snapper+st2446-00+rebuild+carburetor&tbm=isch&ved=2ahUKEwiojbSc0I3xAhVPZKwKHZyaA7wQ2-cCegQIABAA&oq=snapper+st2446-00+rebuild+carburetor&gs_lcp=CgNpbWcQAzoECCMQJ1Cgtg1YirUOYL23DmgCcAB4AIABrQGIAfYTkgEEMjYuNJgBAKABAaoBC2d3cy13aXotaW1nwAEB&sclient=img&ei=rVDCYOiCJc_IsQWctY7gCw&rlz=1C1QJDB_enCA643CA644&safe=off

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carburetor bowl already has water in it,
1 dump it wipe it.
2 flush line between tank and carb
3 also thru carb

Sounds like the carburetor/diaphragm is in need of attention..
These little carbs are sensitive.. take it to a qualified professional..

Perhaps something is stuck in the throttle actuator, or perhaps the carburetor is loose. Check the bolts or screws that hold it on the motor block, but if they are very loose, you probably should replace the gasket(s)!

best thing to do is drain the gas and blow out the fuel lines. take the carburetor of and clean it real good with carburetor cleaner. there is something in the bowl interrupting fuel flow.

It sounds very much like the carburetor's float valve is stuck shut, not allowing gasoline to enter the carburetor. Try tapping on the side of the carburetor several times with a screwdriver handle while a helper cranks the engine.

It's also possible that the choke isn't closing for a cold start, or that someone has fiddled with your idle mix screw, turning it fully closed. If you're SURE that nobody has tampered with the idle mix screw, it may be time to pull the carburetor off for a thorough internal cleaning & possibly a rebuild kit.

Remove carburetor, spray with air, use medium stiffness wire brush, replace seals and reassemble

the choke is controlled by a rod that goes to the muffler it's a open or closed thing see a lot more problems with dirty carbs and the needle valve seats swelling from the fuel

The carb. is working. Get a carb. kit and in it. They don't cost much.

Check battery cable connections to make sure they are all tight. It may be getting hot from trying to start for to long. Also try starting with starting fluid. If it starts with starting fluid you probably need some work done to carburetor.