I’ve previously read that it implies the survival of a Cymbric population in Anglo-Saxon territory, which is consistent with it’s use in, for example, Elmetsaetan in (I believe) the Tribal Hidage, Elmet having been a Welsh kingdom into the 7th Century, and it’s used mainly in other places on the Western frontier of Anglo-Saxon territory. However, Stenton’s “Anglo-Saxon England” doesn’t mention this and treats things like the Tomsaetan and Magonsaetan as just another Anglian territory.
My guess would be that the ‘s’ in Elmetsaetan, etc might be possessive - so it’s the “aetan” of Elmet, the “aetan” of Tom (the Tame), etc.
And a wild conjecture says that just possibly “aetan” shares an Indo-European root with the Greek “ethnos”, people, nation. So it’s the people of Elmet, i.e. the people who live in Elmet.
But whether “aetan” comes through Cymbric languages, or through another route, I can’t say. If it does come through Cymbric, it doesn’t necessarily imply the survival of a Cymbric culture; the Anglo-Saxons could have named these new territories after the people they had conquered and supplanted in each of them.
By “Cymbric” do you mean Welsh specifically, or Brythonic in general?
According to this Anglo-Saxon dictionary, saeten means something like “inhabitants.”
Also, the old name for Somerset here (“Seo-mere-saetan”) is translated as “dwellers by the sea lakes,” so that agrees with the “inhabitants” translation above.
(Although that’s not the usual explanation of the name. You can find the more accepted etymology here). At any rate, even in that etymology it looks like the saete ending still means something like “dwellers” or “inhabitants,” but probably in a different inflection. I don’t know enough about the grammar of Anglo-Saxon to say definitively, though.
This source says that it essentially means “settlers” and that it refers to areas which came under English control later. So it refers to the English, not the Britons, but it does imply what you said in your OP.