The iOS 14.5 beta update that was released today introduces support for the latest gaming controllers from Sony and Microsoft, allowing the PS5 DualSense controller and the Xbox Series X controller to be used with iPhones and iPads.
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An earlier iOS 14 beta suggested that support for the updated controllers was in the works, but it will go live in iOS 14.5. It's also likely that the accompanying tvOS update, tvOS 14.5, is gaining support for the controllers.
Apple Arcade games and other iOS games that support controllers will be compatible with the PS5 DualSense and Xbox Series X controller options. iOS 14.5 is limited to developers at the current time, but Apple will likely have a public beta coming soon, with the update set to be released in the early spring.
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I've got to believe it'll be included in tvOS 14.5 and might be present in the beta already. Apple currently supports the same controllers on all devices according to their support page:
https://support.apple.com/en-us/HT210414
And I imagine they will want to keep it that way to avoid confusion.
Edit: it is indeed working in the tvOS 14.5 beta:
https://forums.macrumors.com/threads/apple-seeds-first-beta-of-tvos-14-5-to-developers.2282875/?post=29564354#post-29564354