I'm struggling with the idea that the continuum hypothesis does indeed have a purely mathemathical/set theoretical meaning, but is neither provable nor disprovable in ZFC (according to Gödel and Cohen). Moreover, CH is not self-referential, like the Gödel and Rosser sentences are.
So why isn't it considered an example of a non-metamathematical undecidable sentence, so that we consider the Paris-Harrington sentence to be the first one with purely mathematical content? Where is my misunderstading?
The notion of a "purely mathematical" statement is highly subjective. It's certainly intended to rule out sentences which arise via "encoding" techniques a la Godel/Rosser/Kleene/etc., but it may be taken further. In particular, I think reasonable people (who grant in the first place that "purely mathematical" is an adjectival phrase worth having) could disagree over whether $\mathsf{CH}$ is indeed purely mathematical. The strictest approach would be something like:
and one might argue that $\mathsf{CH}$ should not be considered purely mathematical according to this criterion on the grounds that, while it does occasionally crop up outside of logic, it does so very rarely and generally indicates that a certain question isn't really the "right" one. Moreover, theorems like Shoenfield absoluteness show that in a precise sense $\mathsf{CH}$ can't have consequences for "concrete" mathematics.
By contrast, this same hypothetical one might argue, Paris-Harrington is very obviously "just" a problem of pure combinatorics. In fact, the only thing connecting it with logic is its unprovability analysis - it's not a sentence from logic, it's a sentence about which logic has a lot to say.
Of course all of this is highly subjective, and quite frankly I don't put much stock in the notion to begin with. But this is what's behind the attitude that $\mathsf{PH}$ has a distinguished status as a natural undecidable (in $\mathsf{PA}$ rather than $\mathsf{ZFC}$, however) sentence which $\mathsf{CH}$ lacks, which is what the OP asked.