It’s 80-90% of the products that requires you to rewrite the Barcode 1-2 times. It’s very frustrating as everything else gets picked up easily. I have a lot of products & managing these codes after adding 5 new products can take an hour depending on how many variants there are, as well as having to find & re-enter the barcodes for those lost in the listing process. Fix this please!
I recommend you contact Google Support who deals with these specific bugs here: https://support.google.com/merchants/contact/shopify_3p_support_app
However, in all honesty the Google and youtube app has a lot of bugs, with little to no functionality. So you will always have some limitations. For my clients, I always use: https://apps.shopify.com/multiple-google-shopping-feeds
If there’s 1 thing we can learn from this is that nothing is free. 
However there’s also an issue from shopify as well, the barcodes can get lost in the save listing process. There it’s only 20-25% of the time though. For some reason barcodes seem to be super buggy on platforms in general(?)
I wonder what makes barcodes so hard to register.
If you think about it, getting paid is a great motivation to providing a service with satisfactory results. While, yes Google has provided an app, because it’s free, they have there goals set differently then what customers want. And rely on AI to do most, which does not understand human frustration
I have not heard of the barcodes getting lost in Shopify, that sounds like you should record the issue and share this with Shopify support.
I should do that