It seems we have a libvirt PKGBUILD but no released package. Here is the MSYS2 approach to software development, shamelessly taken from ArchLinux. Could you try this:
even if it does work, file a bug asking that mingw-w64-libvert gets packaged.
You really should not mix binaries from different ecosystems and compilers. I do not know how TDM configure their compilers or how Fedora configures theirs (exception models, C++ ABIs) but it is a risky business and I caution strongly against it. All your packages should be compiled with the same toolchain.
Why would you use TDM compilers anyway? MSYS2 comes with its own: pacman -S mingw-w64-x86_64-toolchain gets you the 64-bit version.
Just use MSYS2. It is all that you need. Can you explain why you would do this?