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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

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!
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.