Create a new .cmd (e.g., terminalenv.cmd) inside your OMNET root directory (e.g., /c/omnet/omnet-v5.6.2/) next to the default mingwenv.cmd and insert the following commands:
@echo off
setlocal
set HOME=%~dp0
call "%HOME%\tools\win64\msys2_shell.cmd" -mingw64 -defterm -here -no-start
They call the packaged msys environment shipped with omnet with specific parameters to directly launch it in a windows terminal windows. The HOME environment variable allows to run OMNET commands directly.
Test if everything works by launching the cmd, which should open a Windows Terminal with the msys environment, and try launching omnetpp, for example.
You can also create a profile in the terminal that allows you to launch omnetpp env from an open windows terminal window. Add a new profile in the terminal settings and enter the termianlenv.cmd as command line call (e.g., C:\omnet\omnetpp-5.5.1\terminalenv.cmd). Here, you can also set a launch directory, e.g., to your omnet workspace.
I have tested it with OMNeT++ Version 5.5.1 and 5.6.2.