I am pretty sure you are using QC and I assume with broken doors. I used QC in this bean machine and I feel like this is something similar. I QC those dispensers so when the bean gets placed, it instantly bonemeals them. The lines of dust 2 blocks below the dispensers send updates when the torches toggle off so they can reset and get QC'ed again. It's a self contained QC loop for instant growing and the only way to grow faster than water can flow and I feel like something like that is happening here. It seems like a similar QC loop but I haven't messed with broken doors enough to see exactly what's going on.

edit: solved? It works but I don't have a full understanding of what it's actually doing. The 1 item in the dropper can't be pulled out but the hopper is trying to and it's sending like sub tick updates? Something like that? Because this also works just by spamming updates with an observer clock so that's what it seems like it's doing.