When I click the Search button and change it to Projects I would like to be able to type a word and have a list of the projects with this word in it appear in the main menu.
For instance, all my Circuit-related projects, start with "CIRCUIT - xxx". I would like to use the Search button and have only the CIRCUIT projects appear.
From a Project view, the only Show option are "Archived".
What you are describing happens for in in a floating window just below the search field (on Chrome). Are you not seeing that or do you want the main projects on the fully page to dynamically filter. If it is the second then maybe this is a feature request for the task page filter. Currently it lets you pick a single project or a person a task is assigned to, but it doesn't take a string like the search does.