FZS600 - No power, won't go faster than 50, engine not smooth

[Torque]

OK so I have fitted carbs back. I've turned off then turned on the ignition twice, so pump built some pressure.
After igniting about 6-7 times for 3-4 seconds bike started to give some noise, then ignited, but only 1 and 4 cylinder were working.
I've checked and one of the coils was connected in the wrong way. After I've connected coil back, bike ignited on 4 cylinders.
However still issue exists.

So I have checked fuel level in float tanks in carbs. I've only checked 1,2 and 4 cylinder since could not fit the plastic hose because of starter motor (below the carb). Fuel level was fine.

I've also checked the air filter and it was not clogged.

I have no ideas what could be wrong. Bike starts and runs fine, but if you add gas quickly it dies.
I've also noticed that it runs much better when choke is enabled (you can add gas quickly and it won't die), so I think it's under fuelling?
I can't understand it how bike can run very fine one day and be not driveable the other day? I would understand if it started slightly stuttering, but this is terrible.

Basically I've gave up today and totally have no ideas about that.