Some reveals and implications from the 6.55 MSQ.
The MSQ pre-empts all our questions about whether the Scions should participate in the succession ritual by explicitly saying outsiders are encouraged to participate. And even then, the WoL and G'raha can express caution at getting involved with politics anyway. The end decision is to go to Tural to see the situation first-hand, and decide from there; I think this is entirely fair and reasonable, even if Doylistically we know we'll be getting involved anyway.
As it turns out, the "client" that Thancred and Urianger were talking about is not Wuk Lamat, and likely not Gulool Ja Ja either. Wuk Lamat specifically wants the WoL, or rather "the strongest champion". So the Archon-seeking client is probably another one of the four claimants to the throne. Wuk Lamat's faction is primarily the WoL (and Erenville), plus Krile and the Leveilleur twins tagging along, the former to find out about the letter to Galuf and the latter to essentially sightsee. This does mean Estinien still doesn't really have a real reason to follow to Tural; I suspect it is surprisingly plausible he's going to turn up there just because he figures he can find work there, completely unrelated to the rest of the succession ritual. I just watched the post-credits scene: Estinien is literally going to Tural because he has nothing better to do.
The Miqo'te in the expansion art is likely Koana, Wuk Lamat's adoptive brother. "Second oldest brother", apparently. He's also likely another of the claimants to the throne. In fact, given we see five "new" characters in the expansion art, those are probably Gulool Ja Ja (obvious big Mamool Ja with two heads) and the four claimants.
Wuk Lamat says there is one particular claimant out of the four who must not succeed the throne. She uses male pronouns for this person, so it could be the Mamool Ja in the front row. Going further into speculation, this is probably the "eldest brother", and may be the "trueborn" son of Gulool Ja Ja. The other option for the "must not succeed the throne" character is Koana, but the way Wuk Lamat and Erenville were talking about him, they don't seem to be angry or sad, so I think it's less likely.
This leaves the woman at the top of the expansion art as the complete unknown. I am speculating she's the fourth claimant to the throne. Possibly Wuk Lamat's adopted little sister?
Completely baseless speculation: the way the woman at the top is posed, and the lack of information we have on her, makes me think she's either the true villain who's manipulating everyone into thinking the other claimant is the expansionist ambitious one, or she's the meek yet wise little sister type who ends up winning the succession as everyone else withdraws peacefully. I have no basis for this other than "vibes" and "it would be the sort of story I expect".