New and unique opportunities now exist to look for technosignatures (TS) beyond traditional SETI radio searches, motivated by tremendous advances in exoplanet science and observing capabilities in recent years. Space agencies, both public and private, may be particularly interested in learning about the community's views as to the optimal methods for future TS searches with current or forthcoming technology. This report is an effort in that direction. We put forward a set of possible mission concepts designed to search for TS, although the data supplied by such missions would also benefit other areas of astrophysics. We introduce a novel framework to analyze a broad diversity of TS in a quantitative manner. This framework is based on the concept of ichnoscale, which is a new parameter related to the scale of a TS cosmic footprint, together with the number of potential targets where such TS can be searched for, and whether or not it is continuous in time.