1987 Yamaha Riva XC125 starts high then falls to low rpms and stalls out slowly after a rough idle

Intro:
Hi guys, I wanted to start by letting you all know that I’m new to motorcycles and just vehicle repairs in general and this is my first bike. I believe I have reached the point where my lack of experience is a wall to fixing this, please help.

Vehicle History
I got it cheap from a coworkers family member $200 bucks. When I received it, it started up and ran and I was told it just needed an oil change. I failed to ask more relevant questions being new to this whole process. Suffice it to say since receiving it, I’ve found it was poorly maintained by PO. Since getting the bike I have done: Valve adjustment, changed tires, spark plugs, brand new gel battery, fixed wiring and electrical issues, new battery, motor oil and final gear oil change.

Potentially relevant information: This motorscooter is carbureted by a Teikei 22 carb and has a vacuum petcock. The clutch is automatic. I’ve read elsewhere that the carburetor design is apparently a stupidly complex one that Yamaha moved away from in later models and that the electric starter tends to fail.

History of current motorcycle problem:
Last week things were running just fine then when I got home and hit the kill switch and turned the ignition key off the bike was still combusting. While sitting there I nudged the throttle on accident and it seemed to stop.
Next morning I could not start the vehicle and as I continued to attempt to start it, eventually it stopped turning over altogether. I didn’t have time to deal with it so I left it as is till the next morning. I attempted to start it again with no luck and noticed a leak under the bike. I discovered that the bike was pouring massive amounts of fuel into the air box and crank case. That day I took off the carb and checked the float, I discovered that the float plunger was frequently getting stuck when upright and would not close all the way. I adjusted the float until it closed properly when upright and adjusted the floats to the proper level. I then did light cleaning of the carb by spraying carb cleaner through everything and blowing it out with air. After re-assembly I changed the oil cold and attempted to start.
The bike is now having issues starting. It will turn over and combust then quickly die out. I found if I start the bike while holding the throttle full open it starts up easily but immediately revs to high RPMs then quickly falls to low. As I release the throttle slowly it revs back up for a second then idles super rough with the throttle closed before eventually sputtering out and dying. If I give the bike throttle while it’s idling rough the engine will either start to rev up then start to sputter or just die outright. The good news is that it’s no longer spitting gas into the air box.

Here’s a video of me attempting to start the bike, warning it is loud:
https://youtu.be/GxatA-uTYHM

The fresh oil has become cloudy and darker without having ran at all so it’s possible it’s still dripping gas into the crank case but I’m not certain.

I’ve pulled the (brand new) spark plug and found it carbon-fouled.

When I look in the tank, it’s low, but not so low that it should be having issues running.

Does this sound like an obvious problem to anyone? Any suggestions or tests I can perform that might fix it?