LazyPlumbob Are the missing packs specifically ones you bought for PC. as in your first screenshot? Packs you bought for console wouldn't transfer, but maybe you already know that.
If your packs are available to download, you should see them in your EA App library, under Sims 4 > Manage > Manage add-ons. Let me know what you find there.
If the packs aren't listed under Manage add-ons, please contact EA customer support for help. Upload the first screenshot you attached here, the order history on ea.com, plus orders for any other purchases you made for PC that aren't showing up now.
I would strongly suggest selecting live chat rather than email. If you don't see the option, try the "I need help loading my game" category, which usually offers live chat for me. Alternately, try using the help site without being signed in. Some categories of issue allow you to proceed without an active login, and many of those offer the live chat option.