Which personality around people she considers attractive. The moments where she does some flirting with Karlach, or the moments where she's embarrassed about being attracted to PC, giving you a more wholesome dialogue option that gives approval compared to the straightforward dialogue option that just says "lol lets fuck" which.. does not. She also never does anything. Astarion and Lae'zel will fuck around if you don't romance them (implied to happen more than once, even), Wyll will have a cute chat with Lae'zel to her disappointment, Gale and Shadowheart do nothing and Karlach can't.
With the exception of the Mizora dialogue, it is never stated that that is how it is. It is stated multiple times that Shar doesn't want you to be distracted and that they therefore needed to find excuses or do it secretly just to have intimate moments with others, including throughout her entire Sharran act 3 story arc, which I admit isn't much because act 3 is shite, but it's more than a single optional dialogue that happens while she's out of character. There is also absolutely nothing in the House of Grief itself that hints at this being the case either, while there are memories she regains about torturing and infiltration lessons. Meanwhile her relationship with Nocturne is implied to have been entirely platonic. You think if it were encouraged, she wouldn't have a more vivid history with the one person she liked there? It's contradictory no matter how you put it, but at least if the game gave more hints at both then you could argue that it just depends on what she remembers. It doesn't.
I call the entire interaction out of character because so much as kissing Wyll makes her disappointed, and she forces you to choose on the spot. Or even just laying next to Karlach at night, where nothing actually happens. But the only thing she's upset about (if you can even call it that) regarding Mizora is that you didn't ask first. She doesn't even get angry if you tell her you'll do what you want. Absolutely none of the dialogue choices piss her off in the slightest. Why, then, can't you ask her about having an open/poly relationship with Karlach? Or any other origin companion, if she's suddenly fine with an open relationship now while she very clearly wasn't before? Again, if there were more hints than just this one interaction (and the Halsin shitshow), then it'd be more believable. But everything else hints at it not being the case, dating all the way back to act 1.
And I do not AT ALL buy the fact she didn't expect you to stay faithful. She spited her goddess, her only support at the time, just to devote herself fully to someone she apparently didn't even expect to be faithful?
All of the above? Shadowheart's lack of initiative to actively pursue relationships or attachments is honestly probably one more bullet point for why she's so important to the Shar cult she's in. She expresses herself quite openly, but it seems consistent that someone else has to take the first step. As you said, Karlach can't. For all his Act 3 design problems Halsin likely would have if he were an Origin, and his code certainly has him acting the role of pest interjecting himself when he thinks he has a shot to shoot.
In terms of what's stated, there's that pair of rings that have a whole story about a Justiciar who built someone up into loving her completely, enough to accept a ring from her. It was to take advantage of him so he would unwittingly tank damage to help her survive, but the game establishes the precedent of this particular brand of distraction decently enough imo. We don't get basically any exposition about the specifics but between that, Shadowheart's comment, and who the current figurehead of the cult in the game happens to be, it all makes sense to me. In my estimation Shadowheart's personal lack of initiative to get some casual fun in the woods (and the way she mentions that if you pitch it to her implies a little past personal experience) is just one more reason she was groomed into such a central role. The player character has to put in a fair amount more effort into assuring her of their sincere interest than pretty much anyone else because she does kind of resist in hopes of being elevated to a position that WILL demand more devotion to Shar, but that's not being demanded of her yet at game start and the more she likes you the less she's willing to pass up the chance while she's able to take it. I think it pretty clear she could easily have ended up liking Karlach enough for that too, and maybe would have even given Gale a chance for at least a dalliance if he ever made a move.
See this I disagree on mostly because as you mention, the Origins were arbitrarily left out of the poly dynamic. Rather than it being out of character for Shadowheart or anyone else for that matter, I see it as a design shortcoming that you can't include anyone else even for example when Karlach fully volunteers herself to be included. Larian decided not to make the effort to fully follow through on that dynamic for reasons only they know, but even if we did know them I bet they'd be equally as baffling as making the endings people expected and deciding not to use them, or rushing the game out a month early.
Certainly she expects faithfulness. And part of that is the expectation that you don't pull shit behind her back which is exactly why she still chastises you about Mizora even while being quite forgiving of it.
-edit- sorry some of this sounds like it's just repeating things you already said in the last few posts, I had to afk in the middle of writing this so I didn't see them until after.
