When nothing matches, the page says No projects match, with what you typed, and Clear search shows them all again.
Projects is a single list across the whole width of the window, one row per project in the style of Conversations, with a thin line between rows and no other view to choose; the page starts like Conversations too, with its title, a short sentence, the green New project button on the right and Search projects as wide as the list. Each row shows the project's icon, its name and the number of updates you have not read yet; clicking it opens the project, and its Activity and ... buttons appear when you point at it.
Who is working shows on the row with a dot: a small green dot next to the name means someone else is working on the project now (one of their agent sessions is open on it, or they changed something in the last 5 minutes); pointing at it says Someone is working on this project. Your own sessions never count, and the dot relies only on recent data from SyncNow's server. See What does a project row in the Projects list show?.