Here's a good article that lists was people think of primary partners / nesting paryners / anchor partners. As Tav likes to say "first in my heart". SH wants to be first in Tav's heart:
And using the terms in that list she feels hurt and jealousy with Mizora but compersion when Tav asks about being with Halsin. To me this seems a very consistent poly principle - ask first, not asking is cheating.
Now you are on to something that SH's desire to "first in Tav's heart" is so strong she might qualify as monogomish*. She only wants Tav to be with people who won't threaten her primary relationship. Karlach is a threat, Halsin is not. Note that she also says no to the twins if she and Tav haven't had sex by themselves first. She wants to establish base camp and then go exploring.
* (and if you start doing some research your will *hundreds* other terms
Hold up, she straight up says no to every proposal, how the hell do you know who she sees "threatening"? Sounds like headcannon. She just says no and thats it, even no to those who she finds attractive or to those who you would describe "poly" or "open". She even knows that Karlach is doomed and attracted to her, but she still says no. Not to mention what she says if you propose Wyll("In fact I don't want to be your spare lover"). And what the hell is that drow convo argument? You can sleep early with Laezel while being in "starting" relationship with SH and she won't say a word.
Lets summarize what we have about poly/mono things in act 1-2: 1.)She shows NO interest in poly relationship if asked directly. Thats just it, stop trying to headcanon anything. 2.)She is flirty but won't sleep with others if not romanced/shows no interest at others. 3.)The only indication that you can classify as "poly" - at tiefling party where she says "not today" if you ask her about sharing a bottle with all friends. But, I may be dumb, how the hell you came into this conclussion. I even rewatched this scene and it's just blatant that she wants you 1v1 and it's funny dialogue choice to play dumb? It doesn't even end with sex or anything.
