Using Homebrew and multiple users is excruciating and an eye opener on how system-level software should really be installed.
Homebrew insists on avoiding root privileges whilst also installing packages system-wide. That works fine and is invisible with one user but falls down hard otherwise.
Their documentation is incorrect too, saying that this is all fine because “we install in /usr/local/bin”. It’s not easy to change this.
The solution was to embrace MacPorts which correctly requires root privileges to install system-wide packages.
I haven’t looked back since. I haven’t missed brew or any software that’s available on brew alone.