While not advertised on Apple's website, it has been discovered that iOS 16 adds support for the Nintendo Switch's Joy-Cons and Pro
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Switch Joycon Controller Holder Compatible with iPhone/iPhone Pro Max, Joy Con Game Controller for Each Size iPhone, Gaming Controller holder kit, Need Upgrade to IOS16 or Above. : Video Games
Apple's iOS 16 Update Supports Switch Joy-Con And Pro Controllers
Dogean Adjustable Mount for Nintendo Switch Joy-Con and iPhone with iOS 16 Joy con attachments Adapter Switch Joy con Controller Holder Compatible for iPhone with ios16 : Video Games