I created a site key with site A.
Applied the key to site B.
Now, when I try to log on to the admin of site B it logs on to the admin of site A - this happens whether trying to log on to the site manually (siteB/wp-admin) or through the MainWP SSO button.
Based on your description of the problem, I assume that you applied the BSM settings to Child Site’s General Settings (/wp-admin/options-general.php)?
If so, the problem was likely caused because the WordPress Address (URL) and Site Address (URL) were overwritten.
Yes, I was on the Child Site’s General Settings (/wp-admin/options-general.php), but the only setting I had changed, before making the key, was the WP core auto-update setting.
If I am correct (it appears that I am not) the documentation and videos (8 years old) show that only the settings you change are recorded in the key you make - - I just looked at the key again and it appears to be correct with ONLY the disabling of the core-major-auto-updates