When interacting with BC.info user interface - the key shows up in "Imported Addresses" and while clicking on "Show private key" on blockchain.info it displays "Unsupported Private Key".
The 33 character private key from 2013 backup is the same as from 2020 backup.
it may not even be a private key. just because the JSON file says "priv" in front of it doesn't make it so.
since it seems like this address is an imported one maybe you imported a bitcoin address and that key (uNKxxxxxxxxxxxxxxxxxxxxxxxxxxxBfM) is some data that corresponds with the address like its 20 byte hash160.
try decoding it with base58check (base-58 encoding with a checksum) and see if it is a valid encoding and what the result is.
don not post the result anywhere just tell us the length of the
byte result, the first byte and the last.
if it is indeed a valid base-58 string with 4 byte checksum and gave you 21 bytes after decoding (1 byte may be the type) then you just have a hash not a private key. and you should be able to see the same 20 bytes if you perform the same decoding on your address (1MHJxxxxxxxxxxxxxxYMwR)