Hello forever-the-luddite,
Thanks for participating in the Apple Support Communities.
We understand you're looking for assistance with your cables not working after using iOS 16 with your iPhone 13 Pro Max, correct?
If we understood that clearly, let's check into both the power adapter and cable to see if either of these may be related to what's happening. With the cable not charging your iPhone, are you using an Apple certified cable, or is this a third-party cable purchased elsewhere? For assistance with checking for a counterfeit or uncertified cable, take a look at this resource: Identify counterfeit or uncertified Lightning connector accessories - Apple Support
If you see that a new cable from Apple isn't lasting longer than a week, try using a different power adapter to see if the results change. If you notice a difference, check if the power adapter is capable of supporting the iPhone 13 Pro Max. For help with determining this, get started here: Power adapters for iPhone - Apple Support
We hope that's able to help isolate where the problem is occurring, and update us with additional details if you need further help. Confirm what cables and adapters you use, and share more details on what occurs with the cable to know it's no longer working.
Have a great day!