Which game controllers are compatible with the iPhone 16 Pro Max?

I'd like to play games on my iPhone, including Netflix Games like Sonic Mania Plus and TMNT: Shredder’s Revenge, as well as other games such as Mario, Lep's World, and Subway Surfers.

Are there any controllers that work well for this purpose? I would also like to use it on my iPad Air 5 occasionally.

Thank you