You can add an obersavtion to the project if you open the desired observation. There you should see a field on the right side with the heading “Projects” (red rectangle):
You can click on “Add to a project”, then enter the name of you project, and select it. Done.
This tutorial from the forum also explains how to add observations to projects: tutorial adding obs.
And I found a thread about deleting observations from a project: tutorial deleting obs