Thank you for reaching out to the community about that. By default, the product page will land on whichever variant is listed first in your admin. However, you can input some code snippets into your theme in order to hide variants when they become sold out. What theme are you using?
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With regards to what to show. If a product is out of stock, Google will not advertise this on the Shopping channel, there may be some delay between data feed updating and Google Ads. Mostly 2 to 3 hours.
You can double check the info is correct by going to Google Merchant Center > Products > All Products > click on the specific products.