iphone X and iphone 11 lag after upgrade to iOS 16

There may be several reasons due to which an iPhone may behave as described by you. Some of them could be...

1. Storage could be an issue --> How to check the storage on your iPhone, iPad, and iPod touch
2. Incorrect handling of the iPhone --> Important handling information for iPhone - Apple Support
3. Dust ingress into the iPhone - Cleaning your iPhone - Apple Support
4. Water / Liquid entry into the iPhone---> Important safety information for iPhone - Apple Support
5. Overheating due to exposure to the temperature beyond -20º and 45º C (-4º to 113º F). especially in the car because temperatures in parked cars can exceed this range -- Keeping iPhone, iPad, and iPod touch within acceptable ...
6. Service of an iPhone by an un-authorised service personnel / agency / store
7. Modification / Alteration of an iPhone by a third party vendor
8. iPhone is Jailbroken

Check your battery health. Settings>Battery>Battery Health>Maximium Capacity. If it's near or below 80%, the phone will not be capable of optimal performance and the battery needs to be replaced.

Obviously, battery health is not the cause of your issue. But as these sorts of issues can be caused by many different things, it might be the cause of someone else's.