Type into the search dialog a snippet of text (NOT CaSe sEnSiTive) that matches the Project that you are looking for.
As in the previous Tempest-Time design, the list of projects is populated from the associated user's assigned projects. If a project does not appear in this list, the user is not assigned to it. Contact your admin user to have them assign the project.
Select the project and then the task and complete the time entry.