Not sure if it's the same bug, but I noticed I still only have level 1 parts after unlocking a lot of them. So after unlocking another few, I checked parts and I noticed an orange dot flashing on some locked parts... IIRC the orange dot means it's newly unlocked.
Edit: Huh, weird, it seems to be refreshing after changing category to another weapon and back. But not between swords I think. When I switched to axe and back to sword, it updated.
The screenshot is from before I figured out the refreshing.