Every picture contains some amount of noise. It should at least in theory be equivalent to the Halting problem to decide whether this noise was generated by an algorithm or truly random.

But there's a lot of practical issues here. If you just add noise then it may raise suspicion merely by there being more noise than expected. So you may need to "move the existing noise around" or remove the existing noise which gets more problematic to do without leaving artifacts. And of course most of the noise may actually be following some patterns that means that the added/substituted noise must also correctly follow as not not raise suspicion.

Couldn't you in theory solve it by using high quality originals and manipulate the compression algorithm to introduce controlled noise that then decodes to your message? That way you can make the noise look more natural than with approaches like modifying existing compressed files.

Exactly. I don't know enough about the topic personally, but I'm genuinely curious if stenography is detectable enough to provide a viable list of targets.

Yes, steganalysis is used to flag material is irregular based on a number of factors:

https://en.m.wikipedia.org/wiki/Steganalysis

Thanks!