Did you purchase and use a story skip (Tales of Adventure: Shadowbringers)? If so,
Tales of Adventure: Shadowbringers will complete all quests for the designated job, up to and including the relevant role quests in Shadowbringers.
That's true even if your jobs were below level 80 at the time you purchased the skip though from the way it's worded, it sounds like it should only affect one of the role quest chains though it's possible it affects all.
Regardless of whether you used a skip, your first step should be to check the quest Journal. Click the Complete button, select Class/Job Quests, then scroll to the bottom of the drop down menu to Role Quests and see if any quests are listed there. I see you have at least one job in each of the role types leveled to 80 or higher so there's a chance you had done the initial quests at some point in the past and the NPCs have moved away from the Wandering Stair to subsequent locations. If so:
Magical Ranged DPS quests are continued
Physical DPS quests are continued
at an isolated shack southeast of Wright.
Tank quests are continued
first in Wright then in Pla Enni.
Healer quests are mainly at the Wandering Stair
but will finish at Tomra.
If any of the chains are showing complete (will have the level 80 quest listed), I can't explain why they are not appearing in NG+ for you. They are added individually after completion of each role type. I've checked my alts that only did one or two of the role quests to confirm.