The sigh of relief makes no sense
This movie makes a BIG DEAL out of its premise; a man should be able to select his own wife, and you shouldn't share your kingdom with a 'beautiful fool'.
When you look at the 'tiktoks' of today, you can realize how wrong the prince is for even wanting a wife, but putting ALL that aside..
This man is HELL-BENT on finding his own wife. Can we agree on that? HE ABSOLUTELY wants to choose, make his own choice, select for himself, find and get a woman that will arouse his intellect as well as his loins.
Then we suddenly get this OVER-USED trope of presenting someone 'disgusting' and have someone else get really scared, as in 'do I have to marry THAT?!' - only to be shown that the REAL individual was someone else, and at this point the 'victim of forced marriage' (or whatever) sighs of relief.
"Phew, it wasn't her!"
However, think about it. Think hard. Do you get what's wrong with this?
What does it MATTER what the 'wife to be' looks like or is dressed like, how fat or old or WHATEVER she is, when he is HELL-BENT on not accepting her as his wife anyway?
He's not gonna marry an 'arranged woman' in any case, so why would it matter if she's fat, old, ugly, etc.? SO WHY WOULD HE SIGH OF RELIEF WHEN HE KNOWS HE'S NOT GONNA MARRY HER ANYWAY?!
AAGH!
I wish movies made sense..