Diagnosing & sorting-through carb issues can be confusing enough, hands-on. Via text, it's slower and sometimes more confusing. That's why I'm taking this in steps.
Okay...at this point, we've isolated the foam as being an airflow restriction. The next question is "why?". Jumping ahead, the follow-up question...is the flow restriction "normal" i.e. within spec for a new, clean, airfilter element? If this is an old foam element, I'd recommend sourcing a new one. If it's brand-new, move onto the next step...the carburetor.
A restriction that's upstream of the carb could be expected to mimic use of the choke. But, there's a fly in that ointment...the airbleed orifices, located inside the airhorn; the choke butterfly leaves those exposed. And that's where things are murky...for the moment. Those airbleeds are needed to get fuel drawn into both (pilot and main) fuel circuits. The pilot airbleed adjusting screw allows you to fine-tune the amount of air entering the pilot (idle) circuit. Turning it counterclockwise, allows more air which leans-out the mixture; turning it clockwise does the opposite. The adjustments have their limits. Around 1/2 turn out, airflow is cut off and the pilot circuit goes dead lean; It's airflow, through the circuit, that pulls fuel from the bowl, through the jet. Somewhere around 3 turns out, the pilot circuit is as lean as it's going to get...i.e. open...if it needs to be leaner, a smaller pilot jet has to be swapped-in. With the main circuit, there is no way to adjust the airbleed. Thus, airbleeds must be sized just as precisely as the jets; they are, in reality, "air jets".
Fortunately, the main circuit is more forgiving than the pilot. The adjustment is jet needle height. Setting the jet needle C-clip into a lower groove richens the mixture; higher grooves lean-out the mixture. The effects are most pronounced at part-throttle. The problem, from my end, is that you're describing textbook symptoms of lean air:fuel mixture...yet we expect the choke-like effect of a clogged airfilter to make the mixture richer; that's what a choke does, right? The logical explanation for this seeming contradiction is that the airfilter assembly is restricting airflow ahead of the carb...affecting the airbleeds. With only the basic knowledge and workshop equipment to which most (virtually all of us) have access, trial-and-error testing is all we have to work with. It can be slow going but, gets the job done...eventually.
Moving back toward simpler & clearer steps, move the jet needle C-clip to the lowest groove and see what it does. It should result in an overrich mixture. Overrich mixtures usually manifest as easy cold-starting and strong throttle response...as well as misfiring at WOT & high rpm. It's probably worth testing with the C-clip in the highest groove as well, the leanest setting, for the experience. It should weaken throttle response, increase bogging and make cold-starting more difficult.
A caveat, for now...I've no idea if your carb is truly clean. Clogged emulsion tube orifices are very common with all of these carbs. And, Z50 carbs are a little different than what's on the CT70s. Those press-in jets can be restricted even after an otherwise thorough carb cleaning...garbage tends to collect between the end of the jets and the carb body, something that is easily and likely overlooked by anyone without years of experience working with these little carbs.
That, I think, spills enough worms from the proverbial can, for now. Take this in steps. That'll avoid confusion and, when the solution is found, you'll have isolated the problem, which is good info to store away for future use.
