This is a really intriguing idea for an app, but I'm not sure how long it can last. If the algorithm for de-obfuscating the messages is known, the regime could just try applying it to every plaintext message they observe, and stopping after the first decoding error, which might be just a couple of words.
A smart obfuscation algorithm would rely on a pre-shared key, such that all possible keys would have to be tried to determine whether a given message was the output of the algorithm. However, all the simple ways of doing that would produce outputs which have statistical/grammatical properties that make the text very different from natural language.
So it wouldn't be too hard to train an AI on, say, a million samples of genuine messages (a corpus built from mass surveillance, or public forums) and another million samples of the output of the algorithm, given the first corpus as input. Once trained, the classifier should be able to detect obfuscated outputs without needing the accompanying secrets.
The next step in this arms race would be for the app's algorithm to use a language model like GPT-3 that generates output with the same statistical properties as natural language, while keeping the hidden meaning and without inflating the size of the output too much. Presumably the algorithm would have to be deterministic in order to be easily reversible (and thus require a "temperature" setting of zero), but it could use a pseudo-random number generator seeded from the shared secret.
