Certainly not any sort of wallet or key identifier that I have ever seen before...

It's possible that the website or service you used for generating them was using them as some sort of extra encryption or recovery mechanism or custom transaction identifier... but without knowing what the website/service actually was, it's going to be mighty difficult figuring out the process required.

And your mails didn't include anything like addresses or transaction IDs? Just the 64 char hex string and the 40(5x8) char string?

Perhaps the 64-character hex string is the SHA256 sum of the "weird" alpha-numerical string, used as a checksum.
That wont tell what the weird string is, however, if it's true, then you can deduce that the 64-character string isn't a private key.

Sorry, I wasn't around in Bitcoin at that time. If you figure it out, I'd love to add it to my [overview] Recover Bitcoin from any old storage format.

Back then, it was blockchain.info. I have a wallet identifier like this: 12345678-1234-1234-1234-1234567890ab (I've only counted the characters between the dashes, it has both numbers and lower-case characters (hex). OP's string looks different.

Just in case: I used to access the wallet through this URL: https://blockchain.info/wallet/12345678-1234-1234-1234-1234567890ab, which doesn't exist anymore. But with this wallet identifier and my password I can still login to blockchain.com. I've never used the wallet to receive anything, so I can't verify if it's really still the same.

Try to turn this into a WIF private key through brainwallet, you might have used it: https://brainwalletx.github.io/
I'd recommend to use it offline.

Which address (script) types have you tested so far?
Have you already tried both compressed and uncompressed WIF?

It makes me think of an old blockchain.com wallet identifier... Not sure if the format is 100% correct tough, but those groupings with dashes in between bring back those memorys...