How to configure the default shell in msys2/mintty?

Try installing the msys2-launcher package with pacman -S msys2-launcher. Then you should have three executables in the MSYS2 installation directory, and you should run the shell using those executables. You can then pin the shell to your Windows taskbar for future launching.

I tried installing msys2-launcher, but could not find the package.

Instead, I updated the Target field in my Windows shortcut to point to the msys2 bash directly:

C:\msys64\usr\bin\mintty.exe /usr/bin/bash