So, customer service just got back to me again and said they "can confirm you've redeemed a code to claim a Google Home Mini as part of your plan in the past. You can check previous orders by going to the Order History page on the Google Store website at https://store.google.com/orderhistory?hl=en-US."
I went to that page, logged in and confirmed that that only thing I've ever bought on there was a Chromecast dongle on October 10, 2017. (According to Wikipedia, the Google Home Mini was released on October 19, 2017.)
But I ordered. no. Google. Home. Mini.
I think a switch to Amazon Music Ultimate is in order....
Same issue, I ordered a Chromecast in 2017 but never a Google Home Mini. Here's my conversation with Spotify in Twitter DMs if anyone's curious what they say about this, they eventually just blew me off.