How to make `sudo su` run startup scripts?
Your information is incorrect. /bin/sh on macOS is actually a real bash shell. The manual you have found is for a Windows program that "mimics" a Linux environment on Windows. It doesn't have anything to do with macOS.

The profile files for bash are:


/etc/profile
~/.bash_profile
~/.bash_login
~/.profile


Note that ~ and $HOME are the same thing. They both mean that it refers to the user's home folder.

The problem you're seeing is because you're using the command sudo su. This means that you use sudo to start su in order to get an interactive non-login shell. This means that the profile files are not executed - instead only .bashrc is executed.

What you want is really a login shell, which would mean that the profile files are executed. You can do that by using the command sudo su - instead.