I'm developing a story set on an exoplanet where a relatively small terraforming expedition is forced to settle on the planet due to some catastrophe 20,000 years before the story's events.
They settled the planet in 4 groups of approximately 3000-5000 on 4 separate large volcanic islands (think Iceland or larger). The habitable area of this planet consists essentially of these 4 large islands (which aren't that close to one another but essentially arranged in a linear fashion) and thousands of smaller islands in between.
Because of the relative lack of accessible mineral and metal resources on the planet, they were not able to maintain advanced electrical technology for more than a few decades after initial settlement.
Since then, the separate cultures have settled into a level of technology between the late Neolithic to early Modern period depending on the type of tech. For instance, metal weaponry and armor would be extremely rare and limited to certain groups, but windmills, sawmills, and even early steam power (for mechanical, not electrical purposes) are available.
Assume that the various cultures have some level of print technology, although the quality and ease of use may vary. So there has been some method of language transmission between generations.
The cultures were geographically separated for approximately 15,000 years until contact was re-established about 5,000 years before the story as the cultures began to spread to smaller islands.
Now that the background is established, here's my question. If the settlers of the planet all shared a common language, what level of mutual intelligibility would be expected after 15-20,000 years, if any?
On Earth, our oldest reconstructable languages are approximately 7000 years old and the level of language diversity is immense. But would that change if they were all diverging from a single, written language?
Maybe the closest analogue in Earth's history would be the Sinitic languages descended from Old Chinese, which has had a relatively standard written version for over 2000 years. Today, the modern Chinese languages form a spectrum of mutual intelligibilty, with more geographically separate languages being less intelligible in their spoken form.
Other things to consider might be the type of script that the common language used. For example, the Chinese script is logographic (each symbol generally represents only one entire word or idea), which means that often different Chinese languages can derive the same meaning from the symbol while using entire different words phonologically. However, if the common language used a very functional, pronunciation-informing script like Hangul (Korean script), would the phonological change be less rapid?