i don't usually go here (omegaverse) BUT. if i did it would not be a static approach to the dynamics.
i think baelor and maekar are both betas. but a specific politically layered kind of targaryen beta.
dynamics change with age, time and context, and just about every king (genderless term) of the seven kingdoms becomes an alpha. the succession is played out as a series of reactions of domination in response to however that process happens. this has lead to several issues over the years, mostly two princes presenting as alpha (dragonlord edition) at the same time. rhaenyra and her brother aegon being a particularly dire case.
notwithstanding alien valyrian costumes of gender-in-waiting even in adulthood, baelor is pushing so much pre-alpha king rizz that it turns everyone's heads. maekar on the other hand is always going to be a beta, always going to be beholding to a higher authority, always going to be weird about it.
dunk is a beta too. as all hedge knights should be. but hedge knight beta is a whole different scope of positioning than royal beta. it's not even close to the same thing. there's a crucial few moments though when he swings alpha and even omega and deconstructs social expectations and the webs of power and leverage that hold up omegaverse as a system of oppression.
this is not something most people do because most people operate on a level of social scrip he is too earnest for. he simply has the range and the kindness to pull this off.
the presentation system of highborn and smallfolk vary and overlap and change constantly and subtly depending on context so that tanselle's puppet show becomes a fertile example of the performance of it all. that is the true subversive element in it: a dornish actress might be omega-flushed and sweet as florian the fool, fill a room as an alpha as a dragon does.
lyonel baratheon presented as an alpha years ago and is incredibly obnoxious about it. sure there's displays of submission to the crown to be done but he's skirting by on a thin thread.
this scenario might be the one au where daeron is happiest for the simple fact that he's an omega and gender expectations include a great deal less jousting and knightly violence, and largely include him sitting pretty and drinking the ashford's good wine, in the understanding that targaryen omegas are this extremely rare living semi mythological callback to valyrian times, when they were the ones to nest and speak with dragon eggs.
he hasn't been married off because all omegas stay in-house everywhere, not just because for targcest reasons. the sheer amount of political negotiation involved in getting his a spouse to multiply with would be huge. but mostly blackraven is keeping him on standby for a possible blackfyre reconciliation (so he says. the big theory is that he's the one from which the prince that was promised will come).
his dragon dreams still suck balls but on the other hand that's largely expected. and at least they are considered serious prophecies to be direly interpreted and studies. and he gets to do ominous jokes about it. so it could be worse.
aerion is not presenting as anything yet. because it would be a shit show if he presented as an alpha but by all intents and purposes he sure does act like one. swerving the other way and leaning hard into the entitled animalistic violent hedonism of it all and claiming lack of presentation as a grey area. very politically incorrect.
valarr on the other hand is actually responsible about his presentation. loading up to present as an alpha eventually but his eventually is going to be only when his own father begins to kick it, in, say, forty years, and so he's got this heir-in-waiting genderlessness beta-but-not-really thing going. historically many heirs-in-waiting have managed to go hard on that (again: rhaenyra. again: aerion, even though he shouldn't count) but vagarr isn't doing anything much with it at this point.
this whole this is going down because sweet little gwin ashford presented as an alpha in the making out of fucking nowhere. and her parents just had to throw a gigantic tourney to very publicly appease the ruling house with a traditional gathering. let her strut around, receive tithe and mark her territory and generally wring every possible political benefit out of it. at the end of it she's supposed to swear fealty to the crown. it's all very exciting!
unclear how much the sheer underlying influence of her teenage pheromones are impacting the general air of neck-breaking amount of new crushes, mood swings and cheerful love of violence around.
egg's current gender is currently 'squire'. btw.