I disagree that RAW is vague; it seems quite clear. The feature says:
You and friendly creatures within 10 feet of you can’t be Frightened while you are conscious.
It doesn't say "can't be affected by the Frightened condition".
A condition is either on you or not. If you have a condition, and then encounter a state where you can't have that condition, then you don't have that condition anymore.
The easiest analogy is to look at a condition describing a physical state. If you're prone, and then the rules say you "can't be prone", then you're not prone. You won't fall prone just because the prohibition effect ends.
The exception is where you're under an effect that applies a condition regularly/continually. For example, if an enemy puts an effect on you that says "for the rest of the encounter, you're Frightened as long as you're holding a weapon" then that effect will continue, even while you can't be affected by its consequences.