The system service manager runs in init_t, which doesn't have permission to follow symbolic links in user home directories (user_home_t). This causes the condition check on the update services to fail even when /home/linuxbrew/.linuxbrew/bin/brew does exist. This prevents the services from ever running.
This can be fixed by running the update/upgrade units from the user service manager instead of the system service manager, which is more appropriate anyway since they run as a specific unprivileged user.