Pathfinder 2E - Dirge of Doom Clarification

So, the question is does Dirge of Doom's frightened condition have any reason to function differently from any other condition?

Specifically, when the Dirge ends does the frightened condition immediately end - or does it end at the affected creature's turns as normal?

If if functions as normal, the following scenario is possible (but not terribly easy to engineer):

• Bard sings Dirge
• Allies go
• Frightened Monsters go
  (Next Round)
• Bard sings Inspire Courage
• Inspired Allies go
• Frightened Monsters go, frightened wears off EOT.

- Repeat

(Note that in bullet #5, the effects of both bardsongs are present - allowing the party to benefit from both songs simultaneously every other conbat turn.)