When using two pair of mechanized airlocks with directional restrictions, the directionality functions if the airlocks are oriented vertically, but not horizontally.
In the example below, dupes path left through the bottom airlock pair and right through the top airlock pair. Jobs queued (e.g. digging) in the ice biome show reachable, and the dupes will go execute the tasks without issues, using the appropriate airlocks to enter and exit.
Here I have the same basic design, but now with the dupes going down through the left pair and up through the right pair. If the restrictions are set to both doors, dupes will not path through to jobs beyond the doors, but the jobs still do not show as unreachable. If dupes are up top and the restrictions are set, they will properly path down through the left pair, but will not path back up through the right pair. If the right pair is set to the opposite direction, dupes still fail to path through upwards, but will path if both directions are permitted on the right door pair.
I have attached the save file for convenience. Jobs are currently queued beyond the airlocks and the door permissions are set to produce the pathing bug.