tl;dr: I'm finding things consistent with my guess that "Larian didn't implement immediate forced movement of Dissonant Whispers because that'd require introducing an entirely new mechanic to BG3."
I believe both the spell fear and the oath breaker feature make enemies run away as their reaction.
I'm finding (mainly by reading the wiki or looking up gameplay videos) that neither of those abilities should make enemies run away as their
reaction. Here I'm using "reaction" as a technical term referring to the game mechanic: a resource you gain once per round at the start of your turn and can be used (or be forced to use) outside of your turn. Dissonant Whispers forces an oppenent to use their reaction to
immediately move away.
The BG3 Fear spell "makes the targets Fearful," which says that you are forced to run away on your turn. Thus, it doesn't use up your reaction and you don't move until your turn comes up. Is this not how it works in the current patch? (This
video as of 7 months ago shows it working as I understand it.)
The BG3 Oathbreaker feature Dreadful Aspect should "frighten nearby enemies," which shouldn't require them run away at all. Is this not how it works in the current patch? (This
video as of 7 months ago shows it working as I understand it.)