In the past, "checking a license key" usually meant Googling a key validator (often an unofficial, shady website) to see if a key was valid or blacklisted. Today, ESET has centralized this. The "new" way to check a key is to tie it to an email address.
The ESET HOME portal is the primary way to manage and verify licenses without having the software open. Access your account at ESET HOME.
If you purchased your license through the official store, you can check details without a full account. Use ESET HOME account | ESET Smart Security Premium
If the key is registered to a different email, a verification link will be sent to that address (valid for 24 hours).