Not to say she is childlike, but the way she denied Frieren her 1st class ranking was petty, and was a demonstration of exactly that - untempered emotions and little impulse control.
My take on this is different.
I think Serie recognize that Frieren is not following her magic philosophy. It would make no sense for her to accept Frieren in her organisation. Neither of them want to work together, but they do not plan to hinder each other lives either. And Frieren only accept to participate to ease Fern concerns. Frieren never really expect to pass, I even think she is somewhat relieved that she did not.
For the 1000 years ban, it is petty. But it is also a joke. The last time they talk to each other was a millennia ago and they do not really miss each other anyway.
When they departed from Kraft, he said "see you in a few centuries". Elfes time is very different.