elements 2021 serial number on box not recognized

What @Greg_S. said.

See also https://helpx.adobe.com/download-install/apps/licensing-activation/serial-number-redemption-code/find-serial-number.html

If you have used the program for more than 30 days after it was initially installed, it was almost certainly registered.  Go to the Products page of your Adobe account and you will find a download link for the program and the registered serial number.

Scan to activate product was  for the retailer, not for the consumer, the end user.  The receipt number?  100% quite useless. 

A key thing I read in the title was "reinstall"- the product should be listed in your adobe account. 

During the purchase process the retailer would first  scan the product bar code, then scan the activation code- the consumer would then take the product home and would find a redemption code inside the package that would be entered on an Adobe website to get the serial number.

I also seem to recall either the serial number being on it's own card, or on a sticker on the dvd evelope.  Not sure which, it is an older product.

A key thing I read in the title was "reinstall"- the product should be listed in your adobe account allready. 
IF YOU REGISTERED THE PRODUCT WITH ADOBE:   Click on your icon on the upper right of this screen. 

CLICK ON MANAGE ACCOUNT. 

CLICK ON PLANS AND PAYMENTS. PSE is listed under the products.   A download  link and the serial number would be listed.

PSE serial numbers ALWAYS START WITH  1057.

BOTTOM LINE:  You are probably out of luck.