This is like a physical version of "I Am Sitting In A Room" [0], a classic work of experimental music. In that piece, Alvin Lucier speaks the words "I am sitting in a room different from the the one you are in now..." into a recorder, which is then played back into another recorder, on and on until it becomes unintelligible.

[0] https://www.youtube.com/watch?v=fAxHlLK3Oyk

Hi, artist here. I also did an interactive installation work directly inspired by I Am Sitting In A Room. :) It's only had a single (prototype) showing though. https://beesbuzz.biz/art/1512-whatwesaidwillbe

See also: https://en.wikipedia.org/wiki/Generation_loss

Whatever scanner they used, it seems terrible for the purpose of scanning teapots.

I used a structure.io sensor (referenced in the text of the post). https://structure.io/

I suppose a 3d-printed object could carry a (steganographic?) copy of its own specification, so you could replicate it endlessly without degeneration.

Only if the specification is concise enough to fit in/on the object. If you're 3d printing a sphere or another shape that can easily be parameterized, great; if you're 3d printing a model of a brain I expect you'll have a hard time.

That doesn't sound entirely trivial? Like a physical quine.

Let S be the original specification.

Let F(S) be the specification with steganography applied. The steganography ensures that there is a Finv that can be induced from F(S) and such that Finv(F(S)) = S.

You print F(S).

The receiver scans the object F(S) and computes S.

From there you can repeat the process.

It's a bit different scanning a teapot to scanning a human - it may be the case that the built-in ability for humans to self-repair could carry the day, even granting that generation loss is an unavoidable thing for teleporters. Interesting artwork though!