There are a bunch of cases in D&D 5e where a spell or effect "doesn't work if a creature is immune to condition X". The most common is "Charmed".
As an example, in the Suggestion spell:
Creatures that can't be charmed are immune to this effect.
As written, "has advantage in making a saving throw against X" has zero impact on spells and effects that say "Creatures that can't be X are immune to this effect".
In prior versions of D&D, such as 4e, spells and effects had keywords. Suggestion would have had the [Charm] keyword, and it would implicitly mean that creatures immune to [Charm] would be immune to it, and creatures with advantage against [Charm] would have advantage against it.
3e also had similar keywords, and even AD&D used them.
5e simplified the rules by removing such keywords. This wasn't completely crazy, because (a) the keywords where never applied everywhere they should be, and (b) the keywords "snuck in" as usually unimportant and where easy to ignore and miss, both when they had minor and major impact. (Ie, invigorating keyword) But the primary reason was blowback against 4e, which relied on keywords more heavily than previous versions.
5e was intended to be a callback to AD&D 1e and Red box and earlier D&D, with "natural language".
Adding clauses stating that a creature has advantage when they are immune to charmed would feel awkward.
That being said
I am aware of zero cases where granting advantage would cause a problem. In every single case I have looked at, advantage would be thematically valid, and in no cases I have looked at would it have a huge balance impact.
The DM is explicitly supposed to grant advantage whenever the situation would warrant it. And a creature with the Brave feature who is resistant to being Frightened having advantage on a saving throw against a fear-based effect is quite probably such a situation.
So advantage on the saving throw here is not mandated by the rules. But rules on when to grant advantage could be read as suggesting it here, and doing so is pretty harmless.
5e design is based off of DM making calls instead of rules-grids covering every case, and advantage is supposed to be one of the mildest tools in the DM's toolbox here. You, as a DM, "fill in the blanks" rather than having all of the blanks pre-filled.
This can sometimes make the game go faster; instead of having to look up the 8 different tags on the effect and how they interact with character features, you look at the effect's description and the feature's description and say "sure, those seem like they should interact", and grant advantage/disadvantage.