Right clicking a villager with a mob bag to pick it up causes the trade menu to be brought up (non-job villagers just shake their head). It is still possible to get them in the mob bag by clicking constantly but this is inefficient.

The villager should be going into the mob bag easily with a singular right click, as the mob bag priority should be higher than the trading priority.

v1.21.6

I have a solution for this, and it will be in the next update