In the lord of Amara fic we know that Cas gets something out of being trapped in the castle with Dean, he gets to "be an omega" but we see Cas still vary much identify as an alpha (wich is completely okay, whatever he's comfortable with) is it because he likes being an alpha, as in he's comfortable with being called and referring himself as an alpha or is it that he was stripped of the choice of being the omega he is that at this point he's just like whatever "I'll be a alpha I guess". What I'm trying to say is... dose he still refers to himself as an alpha because he's comfortable and happy with having that presentation or dose he just identifies as alpha because he was thought that he can be Nothing but alpha?
Cas' feelings about who he is, in terms of designation, are complicated. He had to be an alpha and do his best to "destroy" his omega designation. He is playing a role and he can't stop playing that role.
It's possible that if a witch would have come to him in Amara and said "I can make you a 'real' alpha, no strings attached" he would have done it because he couldn't afford to have feelings and thoughts about the topic.
Even in Gruamach he can't just be an omega. The castle provides him a space to be an omega, to ask questions, to imagine a future where it's known that he is an omega but to everyone else, everywhere else, he is still an alpha. That is still his role.
He's comfortable performing as an alpha because that's all he knows and that is basically who he is anyway. He probably won't change his entire behavior once he is "out" as an omega, trying to live up to stereotypes and expectations.
If the witch came to him now and offered him to be an 'real' alpha he probably wouldn't take it. Also partially because Dean has, to Cas' understanding, offered him an option for a time after he's done being the alpha Lord of Amara. (Of course, this of course raises the question if it's a good idea to make marriage to Dean a condition to being safe as an omega ;3)
Anyway, tl;dr: he still thinks of himself as an alpha because it's basically his job and whole identity outside of Amara. If he had the freedom to be an omega, he would be fine being an omega. Maybe not jubilant about it (because he hasn't had a lot of positive experiences connected to it yet), but fine with it.