To prove that the suction pulling the gas up is due in only a very small amount to the Bernoulli effect, I want you to consider that effect only happens when there is a change in flow area so that under the front of the slide, when it is fully or partially closed, the area is smaller and so the flow is faster than before it and after it and so the Bernoulli effect creates vacuum there which acts mostly on the idle jet which is under the front of the slide. The needle and main jet are before this contracted area but still are at a slightly contracted area being under the middle of the slide. So the Bernoulli effect acts mostly on the idle jet and a little on the needle/main jets. Like I said before, there is some vacuum all the way between the engine and the air filter which acts on the jets, pulling up fuel from the float bowl which is at normal air pressure since the bowl is connected to outside air pressure via a breathing tube.
There is also a vacuum wave which some carbs make extra use of by the raised half shrouds extending up from the needle jet. They catch more of that wave and so the higher the shroud, the smaller the jets need to be.