Polyhedral's hardly new; the Blackburn Skua/Roc had upturned wingtips, if memory serves me.
It's not a question of "anhedral increasing manoeuvrability" - it's a question of designing the configuration to have the optimal balance of stability derivatives - one of which is Cl-beta, aka "dihedral effect", which unsurprisingly is affected by the dihedral/anhedral angle, among other things. For some aircraft anhedral may help, for others it would make something worse. As usual, the only real answer is "it depends..."