I don’t think Likud and IDF leaders care too much about the wellbeing of the hostages, and their behavior pretty clearly reflects that.
They don't, but the Israeli public does. This will matter if a Gaza remains after the war ends.
So if Hamas wants to maximize their bargaining power they should be seeking to undermine the public narratives around the necessity of the war.
Honestly, nobody who doesn't already support Palestine will change their position because they released the 30 or so hostages that are still alive. It'll just be called a move for clout, which won't be too far from the truth. Also during post-war negotiation what's important won't be clout with the international community; that's more of a long-term thing. What they will need then is negotiating power with Israel. Maybe it'll be different if the international community actually takes an active role in negotiations, but we both know that's not happening.