is it possible to extract a "hint hash" of some kind from another hash?
Cryptographic hash functions are designed to have certain properties, which is collision resistance, preimage resistance and second preimage resistance. If those definitions are not clear, we could state informally:

If you only have hash values of some input data, then you can't do anything except check for equality. You can't compare the input data, you can't check if they have a common substring, and most importantly you can't get back the input from the hash. So imagine a hash function as a one-way street, where you can afterwards just check for equality. Any other structure is lost.

And this is the behavior, which is wanted from cryptographic hashes.

So if you consider your database, when you have access to the plain text, you could just use a hash function with only the user ID as input:


$h_1 = hash(FullPlaintext)$
$h_2 = hash(User ID)$
Save tuples $(h_1,h_2)$, e.g. in a table


If you want to add some keys to those inputs, you have to consider that using a different key means getting a different example, and there is no way to tell if just part of the input was equal or not. But with this table you could do your lookups. But it is impossible to get $h_2$ from $h_1$ or vice versa. In a cryptographic hash function, you simply can't go backwards.