Another try:
- Clean uninstall AutoCAD:
https://knowledge.autodesk.com/support/autocad-for-mac/learn-explore/caas/sfdcarticles/sfdcarticles/...
- create new user account on Mac (macOS System Preferences -> Users & Groups -> Add User Account) with admin privileges
- login to this new account and install AutoCAD from it
- activate AutoCAD from this new account using "Enter serial number" option, test how it works

Note: login state xml is created by AdSSO-v2 process which is the single sign on process for Autodesk products, based on the name and location. It contains information about logging in to Autodesk account.