Astarion only needs one person in his life he can trust. He's monogamous. At least Astarion himself would feel much better in a monogamous relationship. Just because a threesome is allowed to do it with him doesn't mean it's in any way good for Astarion himself. The fact that he allows it to be done to himself and even gives some fake theatrical approval is simply because of his affection for Tav, because Tav is the only person who cared about him. Astarion himself certainly doesn't need any Halsin. It's such a "feature" of the game to satisfy the "user" of those who want to have "two guys at the same time".
Astarion has no enthusiastic desire to participate in the brothel, his nervous laughter, his theatrical gestures (hiding his feelings under a mask). He talks about running away if anything, as he once ran from the sun, he already wants to run away, he looks away. This is reminiscent of his behavior in the scene where Tav encourages him to bite Oblodra, there he also pretends and plays before biting, and then he vomits. These are the two situations where Astarion suppresses himself, again, only the brothel situation doesn't lead to a broken relationship. You correctly point out that poly-approving dialogs only occur if the player himself provokes them. Astarion doesn't want to lose Tav, he doesn't value himself enough, realize and protect his boundaries to say otherwise. Astarion is not polyamorous, but a polyamorous Tav can take advantage of Astarion's trauma and Astarion's attachment and push him into a polyamorous relationship. An Astarion without Ascension and an Ascended Astarion are the same person, and of course Astarion will have an unhappy reaction in both, simply because he doesn't like it.
I don't know about Astarion flirting with the girl in the sewers. I've watched different replicas of this scene and I don't see anything that looks like flirting. "Mommy, may I?" That playful line was referring to Tav, the rest of the lines don't look like flirting either. Astarion might have sex with Lae'zel at the party, but only if he's not in a relationship with Tav, and in a relationship he's not paying attention to anyone else.
Astarion would be much happier in a monogamous relationship, I'd say it's the only one he can be happy in. And the "threesome with Halsin" builds precisely because of the player provoking it, Astarion tolerating it because of his attachment to Tav, and the fact that he can't assert his boundaries because of his injury. This opportunity is built on exploiting his vulnerability.
