The Preferred/Default environment settings in Local right now are still for PHP 8.1.9. So when you’re using the Local Connect workflow, if you select to Create a new Site Local automatically sets it to the Preferred values. Eventually, we will probably have those updated to PHP 8.2 but for now if you want your pulled site to use PHP 8.2 you’ll need to take a couple extra steps. What you can do is spin up a new site in Local first, using the Custom method and selecting PHP 8.2.8. Then you’ll pull your WPE site directly into that install instead of selecting Create a new Site. If you go that route the PHP 8.2.8 version will remain.
Regarding the error message, what error message are you getting when you change to PHP 8.2?
Keep us posted and we’d be happy to help further!