I started working for a company that fired a previous IT worker for leaking data.

I can only say the following things:

We use a Firebird DB with an application written by another company, Proxmox, for virtualization of Windows Server 2008 R2, SQL Server, cloud core Mikrotik router, and a few other Mikrotik devices.

I am not 100% sure, but is there some quick way to check if there are some backdoors left, without interrupting internal processes and reformatting everything?

This previous guy was really good, having written software in C++ and C#. I also know that he did some assembler and cracked a few programs in ollydbg.