Hi guys,
It seems I have the same issue. For some reason, Google was not able to see MPN (I have declared EAN in the additional information/arguments for the product, but google is not reading up to there); it’s also moaning about 2 other things (Missing field ‘aggregateRating’ and Missing field ‘review’).
I see you are asking for more details, it’s called Rich Snippets and it seems they are missing from WooCommerce for the moment.
Here you can find the report for 1 of my products on google platform:
https://search.google.com/test/rich-results?id=dAU07cWC19SAl8x9D3sH5Q