Battery draining fast after update: After an update, your iPhone has to complete many tasks in the background, mainly indexing where your iPhone is sorting and managing a searchable database of your millions of bytes of data. This can cause the iPhone to work extra hard and as a result cause they battery to drain faster. After a few days it should go back to normal.
iPhone is “overheating”: When you also use your iPhone, especially running high-intensity tasks, it can once again also generate increased heat. This is all normal. Unless your iPhone is seeing a temperature warning message, which would shut down the iPhone and prevent you from using it, your iPhone is not “overheating”. That heat being generated is rather normal.
iPhone won’t charge: When your iPhone doesn’t charge, this usually means there is debris or lint blocked in the charging port preventing you from plugging in a cord. As a result, use a flashlight and a thin toothpick to carefully get any of that out.
iPhone is slow: Try a Forced Restart to address the lag and performance issues.
Force restart iPhone - Apple Support
Lastly if you’re still having issues, note that your iPhone 16 Pro Max is still under the 1 year limited manufacturers warranty, so I suggest you get service at your nearest Apple Store Genius Bar or Apple Authorized Service Provider.
Genius Bar Reservation and Apple Support Options - Apple