Hard to tell from your first two pics, but it seems maybe the parge and triflex are not enough, or there is something about the water table in the area in question that allows water to seep there over time after heavy rains. I was wondering if you could allow the drywell to let water pass through it to daylight long enough to see if it is causing your issues? By this I mean for you to essentially bypass the drywell with a connected non-perforated pipe to see what happens during and after a big storm. Are your roof gutters doing their job and what are they connected to? Drywell? Run to daylight?
It also doesn't seem you have very much pitch away from the house/foundation, but with just one pic it's hard to tell.
FWIW, I solved a problem of groundwater entering my flip house by excavating out some of the exactly flat grade around the foundation, at existing finished grade; placing a rubberized membrane of 1/8" x 10' x 25' EPDM roll roofing material up the foundation wall about a foot, and out four feet into existing grade/lawn; then I threw down stone on top of the membrane to keep it from being destroyed by UV, etc. I have hardly any slope to the area, but I actually created some by digging down and away as I went from foundation toward lawn, and made the membrane and stone higher at the foundation wall and lower as it went away from same. The membrane came on a 10' wide by 25' roll for around $200-$225. I cut it in half down the middle and laid down 5', (4' out from the foundation wall). With good replaced gutters and downspouts draining to daylight it has worked to keep rain and snow from being able to find it's way along the foundation wall in crevices/fissures that must have cut their way through the foundation soil from years of inattention. I did not tar it to the foundation but may do so this fall to provide a best case seal going forward.
Show us lots more pics and explain what finished state the foundation/basement were at when you started seeing water in the basement.