If Eclipsa had a next closest female relative, sure. If she didn't, then it's Shastacan all the way. But even if she did, during the interim where the next female of kin is either determined and/or searched for, up until she is crowned, Shastacan has royal authority in the transition period. Like say Eclipsa had a sister living in the castle, then sure she could be crowned the same day without confusion. But if they had to look as far as some distant cousin whom lived far away, then Shastacan has to hold it together in the meantime and is the king regnant.
The big spanner in the works is that it seems to be the whole situation and baby swap was very hush hush, which could go in the direction that Shastacan swapped babies and passed Festivia off as Eclipsa's daughter for the purpose of himself not being thrown on his ass when a next of kin female is found. So if in that earlier scenario where like, Eclipsa's sister is right there ready to become queen, and good ol' Shasty comes in all, hold up now here's Princess Festivia daughter of Eclipsa. Then he gets to stick around as regnant king until Festivia comes of age, and also is free to remarry (though of course said new queen would have no heritable right).
So it would be interesting to see how much of a secret the "big secret" baby swap was, if literally only Shastacan and the magic council knew, or if it was perhaps known among the nobility as well and just quietly accepted because no one wanted a half-monster queen. I mean that's also fair grounds for consideration; even if the Mewni monarchy is matrilineal and all, people in the know might have just been like, fuck propriety, we will *never* accept a half-monster even at the cost of legitimacy. Like, how much was it Shastacan's decision of not wanting to be a cuck and raise his wife's daughter to be queen, versus general accepted sentiment of rejecting Meteora regardless and then just hoping history forgets the truth.