The current state of the incarnon progress for this weapon seems to be as follows regardless of stage:
for the first 2ish incarnon progress updates while in a squad, then you can no longer earn progress until you attempt it solo
I’ve had to go through this process to get through the first 3 incarnon forms and I’m currently stuck on the 4th as I was trying to do it in a squad and stopped getting progress before a single game even ended, I haven’t tried it yet but I assume as soon a so go into the mission solo it’ll start working again.