If you’re logging in via Wi-Fi, that shouldn’t transmit your IMEI - but I admit that I don’t know if that’s something they do behind the scenes. They also could just use your IP address if logging in from home. They would be making an assumption you hadn’t sold it (or given it to someone else), but I can see that not being enough assurance.
As such, get a used tablet that you only ever use on public Wi-Fi (i.e. never log it into your home Wi-Fi). I’m sure there are some really cheap old ones on eBay - just make sure it’s on a version of Android the Play Store still supports (I think 6 is the minimum nowadays).
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