SQL Server mirroring between Linux SQL Server instance and Windows Server SQL Server instance

ladislavdvorakasseco 
Hi,
First, I'd like to warn that the technology referred to as "Database mirroring" in MS SQL in specific is not recommended for new deployments, as it's on its way out.

See the note on the top of this page:
Database Mirroring (SQL Server) - SQL Server Database Mirroring | Microsoft Learn

For database replication work, MS instead recommend Availability Groups.

What is an Always On availability group? - SQL Server Always On | Microsoft Learn

They may not perform in the way you want, especially out of the box.
Availability groups on Windows rely on the Windows Server feature Windows Server Failover Cluster, whereas Availability groups on Linux are either clustered using pacemaker
Availability groups for SQL Server on Linux - SQL Server | Microsoft Learn

It is possible, and even mentioned in the previous article, to have availability groups (or Distributed availability Groups) crossing OS boundaries. Linked is the section describing that layout.
Availability groups for SQL Server on Linux - SQL Server | Microsoft Learn

Note that using "Cluster type NONE", which allows an Availability Group to contain SQL Server on both Windows and Linux, only support manual failover.

The second supported scenario is to have both a Windows WSFC cluster and a Linux Pacemaker cluster, and a distributed AG straddling them.
This would also require manual intervention to switch the primary/active between OSes.

Also, make sure you're not reliant on any of the features mentioned in the "Unsupported features and services" section. SQL Server on Linux does not have feature parity with Windows.
Editions and supported features of SQL Server 2019 - Linux - SQL Server | Microsoft Learn