We had Project Professional (specifically 2016 version 1908) running on Windows Server 2012 R2. Initially Project was installed with SharedComputerLicensing enabled. Later we reinstalled it via Office Deployment Tool and shared computer activation disabled in order to utilize volume licensing (rather than subscription).
The problem was a user was getting a license error loop that would repeat every time Project was launched. Project was still usable in this state, but the error was causing confusion. Uninstalling Project and installing fresh did not resolve the issue.
We noticed you just updated your license. Please reboot Microsoft Project for the changes to take effect.
The root cause was this particular user had run Project in the past when it had been installed with SharedComputerLicensing enabled. Deleting the user profile from the system resolved the error loop.