You know something that I haven't seen touched on in the last several pages of this thread I've read (I haven't followed it from the beginning) is that we actually do get evidence that Shadowheart would be open to a poly relationship. If you've been romancing both her and Karlach, you have to choose after Karlach's heart gets fixed in act 2. If you suggest to SH that you don't have to choose between the two of them, (correct me if I'm misremembering) she declines not because she necessarily doesn't want to share you, but because she thinks Karlach deserves to have all of your attention, given her situation. The clear implication being that if Karlach weren't destined to die, Shadowheart would be open to it. And honestly that is a level of concern, thoughtfullness, honesty and emotional maturity that could be the foundation of a functional polyamorous relationship. And we do see throughout that the two of them have solid chemistry together. What stands out most in my mind is Karlach's reaction after Shadowheart betrays Shar. That dialogue alone convinces me that they could work in a relationship and be part of a genuinely healthy and mutually caring polyamorous relationship.
In contrast, the Halsin stuff is pretty much all just horniness and lust and the pair don't demonstrate anywhere near the same kind of bond at all. But it's probably for the best that Larian didn't try to make it work with Karlach and Shadowheart, clearly they lack writers who can see the difference between a genuine polyamorous relationship and a friends with benefits arrangement with extra decoration.
Lets not make complicated more complicated. I think SH tries to hide her own emotions and vulnerabilities and redirects focus on other companion. Anyway, it is funny how SH thoughtfulness contradicts with Halsin lust.