Hi, good to have you here. Welcome!
It can be hard to diagnose this sort of stuff because the bike was sitting, the carb got mucked up, and you've gone into the carb. There are things that can go wrong when putting them back together. You might want to look at this thread and have a look at the videos:https://www.klrforum.com/how-tos-tec...ing-cvk40.html
My first thought from your description is that your idle is too rich. The choke ain't a choke in the conventional sense where it chokes off air to force more fuel in per unit of air, thus reichening the mixture for easier starting. It technically an "enrichener" in that it dumps more fuel into the carb. Same effect, different mechanism.
If your bike stalls when the enrichener is activated then perhaps it is getting so much fuel that it goes way too rich and stalls. That's odd because the KLRs are set up extremely lean from the factory and the pilot jet is almost too small.
That said, a decent starting point for the screw is 2 turns out from gently seated. That doesn't quite hold for the knurled-knob jobbie because it has a different taper to it.
Other things that can go wrong would be an improperly installed main needle, a missing needle jet (they fall out when you're not looking and roll under the bench or down the shop drain), a sticky slide, a torn diaphragm, an improperly seated diaphragm, and so on...
You're in a better position to fix this than we are since it is in front of you, so have a look at that thread and the videos.
Those knurled-knob jobbies are good for adjusting your idle mixture because it's a stone-cold bitch to do it without one, but once it is set they are almost of no further use. Still, I have one and like it.
Popping on decel is normal. It's caused by being lean, which contradicts what I just said, but it's all in "how much
does it pop?". I can make mine pop if I try hard and it sure ain't running lean.