The topic of ambidexterity, beyond the rational case, is born out of Kuhn's \(T(n)\)-local Tate vanishing theorem and Hopkins and Lurie's generalization of this to higher finite groups. This is a topic close to my heart, though I haven't worked much on it precisely.
The closest I've come to contributing to this topic is this paper with Shachar Carmeli, Bastiaan Cnossen and Lior Yanovski where we study a variant of the notion of ambidexterity, based on Klein's dualizing spectrum, and its consequences in character theory.
I do have a decent amount of open questions on the topic that I regularly think about, feel free to reach out to me to discuss some of them.