If your staging site crashes after the update, it confirms that at least one plugin or your theme is incompatible with PHP 8.3. Step 3: Use the Health Check & Troubleshooting Plugin ...

The fact that WordPress itself calls WordPress 5.6 “beta-compatible” with PHP 8 tells you all you need to know regarding whether you should update to PHP 8 or not.

The warnings will contain a link to a WordPress support page with information on how site owners can update their server's underlying PHP version.