"[Astarion] doesn't know how to befriend people. He knows how to manipulate, to an extent, but that doesn't work on Hawke, nor Anders."
Since Anders, Astarion and Gale canonically like cats, I'm imagining conversation sliding that way one night over the campfire. Anders explains almost casually that he wasn't allowed to keep cats for most of his life, during which Astarion is lowkey drawing parallels in his brain, and although still snarky about it he comments that at least Anders gets to pet all the fuzzballs he wishes to now, before telling them a little about Malta, the cat that usually hangs out near Cazador's mansion.
Anders and Gale immediately pounce on that because anything that'll have Astarion be less standoffish is probably a positive and draw him into their conversation, and it takes Astarion several days to realize that wait, this probably counts as A Friendly Conversation, right? Does this make them friends now? Or at least on friendly terms? And he didn't even have to flirt for it or anything???
It would also lead to them including him more naturally in conversation to find more interests they share-- because they have a foothold now.
The downside is this is somehow going to turn to magic and Astarion getting a front row seat to some peak nerding while getting tips on how to use his magic better.