Mutual friends after a breakup aren’t prizes to win. Let them stay friends with both of you.

Treating shared friends as territory puts them in an impossible position and usually loses you some of them. They had their own relationship with each of you, which was never a function of the couple existing. Asking somebody to choose turns a breakup into a campaign, and campaigns tend to be remembered longer than the relationship was. Nobody involved has to lose a friendship over this.

Say plainly, once, that you do not expect anybody to pick. Avoid asking them for information or using them to pass things along. Expect some awkward months and then an arrangement everyone can live with, which is a better outcome than winning.