Quote ”it won't delete any of those pictures as soon as I log into another Lightroom Classic subscription, correct?”
When Lightroom Classic is syncing with your Adobe Creative Cloud a/c you can sync specific Collections from your Lightroom Classic catalog to your cloud storage, the original files will remain on your computer HDD storage.
Original files from you mobile devices and Lightroom cloud-based app on a computer would have synced on to Lightroom Classic and be stored on the designated folder on your computer. I would make sure that LrC sync is paused.
I am also not aware what if any functions you can access through your Adobe Creative Cloud Desktop app if you are signed in.
I am aware that a few of the modules, Develop, Maps are disabled, what about updates, uninstall / install?
I am not aware of any procedure to access your old Adobe a/c from a new Adobe a/c