Thanks for posting. While we don't have news to share as to when exactly will the Nest Learning Thermostat's back plate be available for reorder, our Google Store team is always working on adding more stocks. We suggest that you continue to check back from time to time. You may also reach out to them directly here: https://goo.gle/30F5BRx
I reached out through the link you provided and received no responses. Is there any way that you can confirm that Google is even going to offer these replacement parts anymore? If a 3rd GEN base is no longer being produced then it would greatly assist many of us in making decisions on what we should do with these Nests.
I'm sorry to say, but we here on the forums are unable to check on the stock of the Google Store. The link that Melba provided would be your best bet to find out information regarding what parts are in stock.
Let me know if you have any other questions, we'd be happy to help where we can.