... You know, the Crown Prince's reaction makes me think he wanted Seraphina to get upset and try to oppose the new relationship... Which means this was a play to get her to pursue him again.
FL-chan being involved (and confused herself) means that she probably pitched it to him as such. She doesn't have the existing relationship with the prince for him to actually mean what he said about her.
And since FL-chan doesn't actually know "Seraphina" at this point, she doesn't have any reason to expect her to do anything else. Which means there's a chance that she's actually trying to help him. She seems confused by Seraphina's reaction too. Though it's more likely an attempt to force the "script". It's just... That doesn't really work without the setup? At the very least, the Prince isn't in on it. He seems genuinely crushed by the acceptance of the "rejection"
Like, in reality this reaction is the best one that FL-chan can have. Now she can be the one to pick up the Prince after he's devastated and build "affintiy points" that way. She needs another method since she wasn't around to do so in the first year. If she had predicted this, then getting the Prince to play hard to get with his fiancee would have been a stroke of genius.
Except... She had no way to predict this. She DOESN'T know that Seraphina would be totally ok with breaking up. Which means that her actions are too weird to be self-serving. The "expected result" of this scheme is terrible for her. She hasn't done the setup. And she knows that, she didn't even have enough "affinity" with the prince for him to be genuine in his rejection.