But Fern noticeably underestimates herself.

She doesn't think she's a very accomplished mage, but Frieren does nothing but say encouraging words to her. Fern is very well recognized by the whole "magic society" but probably has no idea herself because she doesn't mingle in those spaces.

We see that most mages grind up through ninth certification to third or so in formal, structured education or in specific jobs. Fern just immediately took Third Rank because it was convenient and passed entirely without issue. She just doesn't recognize that as an accomplishment.

I assume the main reason is that Fern is apprenticed to the greatest mage currently living, and probably the 2nd or 3rd greatest mage to have ever lived, inevitably comparing herself to someone who can't be caught in a human lifetime. Even then, Frieren immediately pointed out that she's lost to quite a number of mages weaker than her.

Fern needs confidence in herself. She hasn't developed it because she's thriving in extremely deadly scenarios on their journey so far.

This is good subtle retroactive worldbuilding.