This is something new. I just create a new project with a new task and I cannot assign the task to the employee. The project has the status Started.
Please assign the Employee to the Project in the Project Team Page, once you done with the Project Team assignment, then the assigned employee will be shown in the Task Page.
Click on Team as highlighted you will be directed to Project Team Page.
Uncheck the Show Selected Employee option so that unassigned/newly added employee will be seen in the Team Page, select the respective employee to be Team member & click on update as shown in below screen.
Once the Employee is added as project Team member he will be shown in the Task Page.