This is possible but you'd have to deploy it right by a black hole: https://en.wikipedia.org/wiki/Photon_sphere

i wonder how sensitive your equipment would need to be to read it from the back scatter off the interstellar medium.

Not a scientist, but I assume the signal would degrade or mutate over time due to space radiation and other radio waves.

Electromagnetic waves have perfect/lossless superposition, so radiation can’t really degrade a signal that way.

The big limiting factors are free space path loss and noise.

That's only true in classical electrodynamics, as it happens. If you're in a very strong B-field like you might find near a compact object you'll get nonlinear QED effects.

You can get a low order correction with Euler-Heisenberg: https://en.wikipedia.org/wiki/Euler%E2%80%93Heisenberg_Lagra...

It should be same logic we use for repeaters, so it'll be fine.

The logic we typically use for repeaters (EDFA, erbium-doped fiber amplifiers) for long-distance lines amplifies but does not clean noise (so across the oceans, you are very much bound by SNR). And you need one of them every 80 km or so in typical fiber.

"Nothing" is a funny name for an interplanetary communication network.

You're still storing your data in the same EM field, just in a slightly different non-inertial reference frame.