For others in my predicament, here is what I learned, and how Google solved this in my case. I spoke to Google customer service, who liaised with the Nest product team about how to address my issue. Total time spent on phone/hold was about 45 minutes. Turns out there is no way to order spare or replacement parts for the Google Nest doorbell (battery version, at least). The "field replaceable unit" is the entire doorbell kit. What I was offered as a solution, and accepted, was for me to order a new doorbell on a replacement basis, with a credit hard hold for the cost, and deactivate and return the old doorbell for a refund under an RMA. This involved some follow up emails. As of this post, I am waiting on the new doorbell to arrive.
To Nest product managers: I hope you'll agree that swapping the entire product on a case by case basis, with intensive human intervention, is not a very scalable solution to the general problem of products breaking or going wrong in the field and needing minor replacement parts - it is uneconomic for both Google and the consumer. Much better to allow a kit of relevant parts/accessories to be ordered as a separate SKU. Thanks to the many Googlers (there were quite a few!) who helped out.
