Hello @bronya,
The older versions of the theme will work with WordPress up to a certain version only. We all know that WordPress keeps getting better and better. They have changed some of the codes that adhere to the latest technologies like Javascript, CSS, or PHP versions. At the moment, WordPress 6.2 is now using PHP 8.x version which is why we also need to update our theme to keep it updated and work flawlessly with WordPress.
All these updates including WordPress core updates were made to ensure security, remove site vulnerabilities and functionalities keep working. All of these updates do not affect any changes made to the site. All your settings, custom functions, and styling will be intact. You just have to clear your caches and regenerate the resources after every update especially if you are using 3rd party optimizing plugins, Cloudflare, and CDN.
We highly recommend that you clone your site to a staging area where you can do all the updates first. It would also be easier to troubleshoot in the staging area. The staging area can also serve as your backup.
Meanwhile, all the X theme versions 10.1.10 and below should work with WordPress 6.1 and below. We recommend updating the X theme to the 10.2.1 version first before updating the WordPress core to 6.2 to prevent the fatal error. All of these should be done in your staging area and once everything is perfectly working, you can proceed to do the updates on your main site.
Best Regards.