Not full-text search, which DBMS to choose?

Question

PostgreSQL

Hello everyone!)
There is a line where incomplete data is stored. the unknown number of characters is replaced by *, you need to find the corresponding string using the full one. This is not quite a basic full text search algorithm. there are no "words". Now this is being solved by "enumeration" of all possible options, which is not flexible and takes a long time. The underlying storage is redis.
Example: "fa*la*" (stored in the database), but found using: "fancylang"
There are not very many records (1-5k). Speed ​​is critical.
Thanks in advance to everyone for your help.

Answer 1

So far, nothing comes to mind except enum for converting the alphabet into a bit field.
First filter by the presence of the alphabet, and then do the reverse application of the pattern to the string.