How to organize a “smooth” transition from one DBMS to another, and is it possible to solve this problem with ETL tools?

Question

Database migration

Hello!

Statement of the problem
There is an "old" system that works with the Firebird DBMS and there is a "new", developed system that works with the PostgreSQL DBMS. The transition from the "old" to the "new" is a process in time, i.e. during this process, both systems are operated, but with one limitation: data changes are carried out only in the "old" system.

Purpose
To ensure the identity/equivalence of data in the database of the "old" and "new" system.

Task
Actually to find the best solution for data migration, which will bring two databases that have different structures (but reflect the same information) into a consistent state.

Now I'm looking towards ETL,

Thank you!