How to log in to different databases based on entering a specific login?

Question

Database

There are 2 databases, the old one from the 90s and the new one from 14 years old, it is necessary that the user enters a certain database when entering the login, i.e. the login page is the same for everyone, but for old users, when entering the login, the road leads to the old database, and new users to new.
How to implement this, are there any ready-made solutions? Which way to look? (I’m zero in this, so I would at least find out the search directions)
As I understand it, you need to make a system that would process the entered login and password, compare it with the list, which user is in which database and, based on this data, would transfer the user to his bd?
Both databases are located on different IPs and servers, and somehow crossing the database is not an option, too different technologies.
I drew a diagram just in case :) cl.ly/Ulht
Thanks for the help.

Answer 1

Make an intermediate database (well, or a config) that will store the binding of users to the desired service.
When authorizing, go and ask this database where to send the user.

Answer 2

Register yourself on all the necessary DBMS and log in under one login