How has it linked with your Amazon account then? Just because you bought the printer from Amazon? (As they do with their own devices, e.g. Fire TV Sticks, of course.)
The printer was purchased at a store called Best Buy.
The only interaction that it has ever had with my Amazon account was that I ordered a single purchase of replacement ink cartridges. The idea of it monitoring their status is abhorrent to me and I don't think I would have ever opted in for such thing. Perhaps there was something requiring me to opt out, but ...it was not apparent.
When my Alexa searched for devices connected to my network, it must have noted this printer, then compared it to the fact I ordered ink for it, and just to be extra helpful decided to monitor its levels for me. I can think of no other way...