Unemployed after 1st postdoc, what should my affiliation be when introduced during campus visit & job talk?

How about "I've done my PhD at [PhD university] with [PhD supervisor], working on [PhD subject]. For my postdoc, I went to [postdoc university] to work with [postdoc supervisor] on [postdoc subject]." If you want, you could also say "I did my postdoc at ...," from which a good reader can infer that your postdoc has ended.

I don't think you need to stress your temporary freelance status any more than that. It's clear enough in your CV and you got an invitation for a campus visit + job talk, so apparently the interviewers do not think it's a big deal. Of course, you should have a good explanation for that gap during on-site interviews.

Finally, try not to worry too much whether you're being invited for fake interviews/to be ridiculed/as a filler candidate. I think mostly you are a bit uncomfortable about your current situation and that's putting some doubt in your mind that (I'm guessing) does not have a basis in reality. Simply concentrate on giving a good talk and having fun chats about the research you'd love to do.

I suggest putting the focus where it belongs, on your work and its merits, which after all were good enough to get you the interview. The affiliation is a purely cosmetic issue and has little significance. Give the best talk you can, and don’t call even more attention to your status than necessary by trying to come up with some creative label (“freelancer”, “independent researcher” or whatnot) to fit some imaginary “affiliation” box that you imagine needs to be filled in the slides or your bio. If asked, tell the truth about your current employment status, but don’t mention it otherwise. Most importantly, as I said, the talk and its contents are what matters, so focus on those things and don’t let yourself be distracted by unimportant trivialities.

Good luck!

I've seen plenty of faculty candidates from industry give academic job talks without an affiliation, so it's not so uncommon, in my opinion to not have an affiliation on the flyers or on the slides.

In part, this choice by these candidates is due to the fact that they are not giving the talk as part of their current industry job, and they most likely do not want their current employer to know that they applied to a different job (they may even request the talk not to be advertised broadly or at all).

As for the second part of your questions, many of the same industry candidates apply for academic jobs well after 4 years from their PhDs. You're most likely not being invited for "fake" interviews. Good luck!

Obviously their reasons are quite different than yours, but like them, you shouldn't worry too much about not having an affiliation.