If it's not the carbs, might be the petcock leaking gas into the vacuum port.
You could unplug the fuel lines and vacuum line and see if fuel pours out. You might have to apply some vacuum and see if fuel comes out only through the lines, but be warned, if you suck on the vacuum hose to apply vacuum you could end up with a mouthful of gas... yes, it happened to me lol.
If all is well there, it's very likely the carbs, probably the floats... should check needles and seats and set the float level.
Why check the petcock first? 'Cause it's the easiest to get to and because taking out the carbs is a pain in the ass.
This happened to my bike at some point... I don't remember 100% but I think it was the petcock leaking through the vacuum port. Anytime I had a carb problem I took the carbs out and did a full cleaning and put them back together... sometimes 2 or 3 times before the problem went away.
1985 VN700 unknown mileage (over 33K)
Iridium spark plugs
NGK wires and caps