Carlota has actually put a lot of thought into what she wants from a husband but it all came out a little depressing. The thing is that she ought to have a lot of children; one of Cheliax's most important present deficiencies is the kinship networks that let the nobility sometimes back down from a war with one another, and there are at least five alliances by marriage she'd arrange if she had anyone to hand out for them. And if she marries a man with a title (and she means to) she'll need a reasonable crop of options for his lands, too, and she's already 27, which is old to be getting started. She ought to plan to spend the next decade continually with child, and she's well aware that this is famously exhausting and might well prove incompatible with running Chelam, defending Chelam, clearing out all the monsters in Chelam, occasionally participating in the kind of high stakes politics in Westcrown where one values the ability to flee a mob as a gas, and otherwise pulling her country together.
Her task is less burdensome if she marries a man without a title, in that she could probably get by with four children not eight, but a man without a title will want to run Chelam, and she finds something particularly dreadful about anticipating the sort of marriage she spends trying to fence her husband out of the political power that is hers by right while, of course, obeying him in all other things as is her duty.
This leaves marrying a man who has his own title and doesn't want Chelam, is powerful enough he can divert some resources towards it if she needs them, and ideally likes her for the person she is at present while also handling it reasonably gracefully if she is too exhausted to keep it up; she prefers that to 'finds the person she is right now vaguely annoying, but will probably like her better once she's too exhausted to do any politicking', even though objectively the latter would be fine, because she does not really want to resent her husband and she worries that she will if he thinks that bearing him eight children and being too tired to do anything else improves her. But then, the only options are someone who'll gracefully tolerate it and someone who'll actively prefer it, and perhaps it's a very dangerous arrogance to look for the first. Blessed Iomedae, show us the path of duty.....ah, actually, You just decided to remain celibate.
Carlota's anxiety about the whole thing has not of course stopped her from politely but unambiguously flirting with the archdukes and Lord Cansellarion. With everyone else she's aimed for good working relationships, but with a mind to which of those good working relationships could turn into a marriage in a pinch.