At first I thought this was just on the alliance side when starting BFA, and you get the first “Listen to X talk” - nothing happens, but suddenly the quest is done after a few minutes.
Now I started the horde side, and just finished my first “Listen to X talk” mission, but there’s no communication, you just have to wait until it’s suddenly done.
Yes, I had this when doing the Zandalari unlock quests, usually only one NPC would talk or both would be silent and then the Q would show as finished. Not sure if it is the same in Shadowlands since I ignore whatever the NPCs say to avoid cluttering my head with bad lore.