The blueprint card for tasks gives the option to +Add to project, folder, or space (for projects it's +Add to folder/project), but that is not possible. The only things that come up in the search window are other blueprints.
I reached out to Support thinking this was a bug; they said it's by design that blueprints can only be added to other blueprints and recommended I bring this up as feedback.
The hyperlinks and labels imply it's possible to add blueprints to spaces, folders, and projects and the popup search text input field says 'Search project, folder, or space'. If that's really not an option, I would recommend revising the text to avoid confusion. Something like '+Add to blueprint' and then 'Search blueprints' in the popup would make more sense than the current text.
Note that the same problem exists in Lightspeed except instead of a hyperlink, the field is labeled Location and the text alternates when selected.