Wasn't Windows NT based on OS/2, which ended up taking over all of Windows starting with 2000 & XP?

Kind of but not really. As I understand it some of the OS/2 dev team at Microsoft was involved in NT (after MS and IBM stopped working on OS/2 together) but they aren't the same code. The NT core is more closely related to DEC VMS than to OS/2. It can be confusing because the name OS/2 was applied to things that are NT at certain points along the way, and NT did have an OS/2 compatibility layer