If you have existing Team Projects set up and then change the VCS Provider in Toad, the following warning message appears:
'Changing VCS Provider settings removes all Team Projects. Are you sure you want to do this?'
The Team Projects are tied to the VCS Provider, and can only exist once the VCS Provider is selected first. Then if the VCS Provider changes, the team projects need to be re-created, so that they exist and are associated to the currently selected VCS Provider. Toad cannot save Team Projects for each VCS Provider, they only exist for the currently selected one.
For example, originally if there was no VCS provider and just Team Coding within Toad was selected, the Team Projects that are/were set up can only exist in that configuration.
If you then change the VCS provider to a 3rd party one like TFVC, that change has to happen first and then Team Projects must be created / re-created for that provider, once it is selected. It is by design, rather than a technical issue in Toad.