I didn't see an explanation for how the -chester suffix became -kaster, as in "Manchester" (en) -> "Mankaster" (nl). Perhaps I missed it?

The -chester means something like "a city or walled town, originally one that had been a Roman station", or sometimes "prehistoric fort". https://en.wikipedia.org/wiki/Chester_(placename_element)

I thought it might be the sound, but I see Worcester (which is the spelling of the unpalatalised variant ) is translated to Workaster, so it's a consistent conversion based on the root.

But if it's etymology, I can't find (at least not with my poor knowledge of Dutch) a Dutch use of -kaster.

A-ha! I think I figured it out! The Dutch village of Kesteren is from the Latin "Castra", for "army camp", https://en.wikipedia.org/wiki/Kesteren .

Well done!