What followed was 4 weeks of calls to Google support. Each time they promised they would reach out to the "shipping partner" and get it sorted. I was also receiving emails threatening to charge me the full cost of the replacement device because I hadn't sent in the broken tablet yet.
Eventually the package got delivered... back to the Google warehouse. Google wasn't aware of this until I called them up - their system assumed it had been delivered to my house. Another promise to fix the situation - and this time they managed to actually get a package to my house. Only it was a Pixel C Keyboard, not a tablet.
Another call, another promise. It's been over a week now and the latest package has not yet been shipped, it's stuck in the order confirmed state.
So, 6 weeks later, still no replacement. Luckily the tablet is mostly for entertainment, I personally plan to never rely on Google for anything important like making a living.