Unfortunately there isn’t an automatic way to update from version 3 to version 4. Version 4 was created mainly for new websites that start now, and it focuses on Gutenberg editor. However you can also use the Classic Editor if you want with the new shortcodes.
As you said, the new shortcode for news is [posts_list] and if you want to show the featured image you should write something like:
Instead of [table_list] you could use [affiliates_table] or [affiliates_list], you can find theme both in our Documentation: https://pokatheme.com/pokatheme-documentation/
Instead of [single_affiliate_xl] you could use [affiliates_single].
“I also needed to add a white background around the text content in articles and reviews, as I had in the previous theme, because here the content shares the unique background and that’s bad.”
– This could be done with CSS, you can use the child theme’s style.css to apply the CSS you want.
About “Article Rating” I’m not sure if this is related to PokaTheme, could you send us more info (e.g. a link)?