If you have made changes to the theme you can use the child theme to maintain your preferences. Keep in mind that you should only update the theme file and not the child theme ok. Now how do I update my downloaded theme here? The answer is simple, you can either use your own server and upload the theme files or you can even use an ftp client to do so. It is not necessary to change your database or anything like that. After uploading the theme files to your server, go to the wordpress admin panel and look for appearance> install plugins and update the old plugins with the latest ones. Hope this helps! I leave here an images of my server for you to see how I do it basically!
In the themes folder inside wp-content I just update the boombox folder and nothing else...
Inside the boombox-child folder is where I make the changes so this is the only folder that I don't change. In other words, you don't need to re-upload this folder or update by the one that comes inside the downloaded package ok ...
Anyway, I am not sure if this is what you have doubts about. But I hope I helped you!