Obsidian file management possibilities are quite limited at the moment.
Please, add ‘New folder with search results’ command to the search result to expand them a bit!
Or, possible, it is better to add something like ‘Select search results in navigation’?
I also agree “Select search results in file navigation” or just “select all search results” being much better option. Moving to a folder (new or existing) can be then done among deletion or bookmarking. Or if Obsidian introduces new actions for multi-selected files, then these actions will be available for search results.