Throttle/carbs issues

[vladgluhovhere]

The butterflies aren’t lubricated by fuel, the float bowls being empty won’t have any effect.
I put a drop of oil as near as possible to each bearing point on the pivot shaft, but if the bank of butterflies turn smoothly and snap back OK when the cables aren’t there that doesn’t sound like the cause.
Silly suggestion: have you checked the right cables are on front and back of the carb pulley?
Only asking because the old cable I have to hand has the chunky adjuster on the return side and your photo shows it mounted on the front.

Pull cable is longer than push, so it makes sense pull goes at the back and push to the front.