the Apple Watch eSIM has its own phone number, for some reason, but it's not one you're supposed to know about

Not a secret if you have AT&T. The watch and its phone number are listed right there in its own section on the bill.

Absurd nightmare situation.

Not unique to Apple Watches, or any other device.

I have a T-Mobile hotspot that was assigned a recycled phone number. It gets several text message receipts each day for someone's Venmo purchases.