The correct way to approach the problem is to distinguish the sources that are found from the process that lead to the sources.
In your comment (which I repeat here only to incorporate it more directly into the question), you suggest that a researcher searches the website of Film Affinity for information about Spanish terror films and series in the preceding two years and finds a lot of useful information. In your example, the information that is found represents the source(s) for the purpose of citation, and they should be cited using whatever citation/referencing system is most appropriate. In contrast, the process of searching would normally be considered to be part of the methodology of the research, and it is in the methodology section of an academic paper that the search process would typically be described.
The duality that you describe (method of finding sources vs. sources actually found) arises frequently in review papers, particularly in the medical sciences where systematic reviews of treatment outcomes are wanted. For a systematic review to be considered useful, there needs to be, as you'd expect, some rational and ideally comprehensive system for locating relevant sources. Without it, there can be no confidence that the sources that have been located are in any way representative of the information available about a treatment approach. One method of conducting and (more particularly) documenting a systematic review is described in great detail on the website of the Cochrane Library, specifically on this page. This paper gives a specific example including descriptions of the method.
