I am using a Windows computer and using Git Bash, I just installed a new 8.8.1 site and also did 'composer require drush/drush'. I can't use Drush from anywhere so I am wondering if I should have installed Drush globally on the computer.
No, you don't install Drush globally anymore. You install the Drush Launcher instead. It will provide you a global
drush command that automagically uses the local Drush from each project.
A small wrapper around Drush for your global $PATH.