I started this post, uh... months ago, and then (believe it or not) kind of lost interest? There's not really a lot to say, unfortunately. It turns out there are three-ish subsets of runes used in the Puzzle House and Kpp'Ar's cane, and while it turns out the overlap between them is small, it does exist. That's about it. Here's a breakdown, though.
The clearest set are the tower runes, because they're very helpfully laid out in Adam Ratcliffe's concept art:
They're included exactly as designed when we see the tower in s7e2:
Then we have Kpp'Ar's cane, which was the main point of comparison I wanted to study. Are the tower runes the same as the cane runes? I ran into two small problems, here: first, it is extremely difficult to get a good look at the cane. Second, the cane's two appearances (s5e2 and s6e6) seem to show exclusively opposite sides of it. I wound up treating their runes as two different subsets as I tried to track whether it was even the same prop model at all. (Jury's still out. It would be weird if it wasn't, but it would also be kind of weird if they just happened to show only two exact opposite angles.)
The cane as seen in s6e6 shares some runes with the tower (green) and introduces some new ones (pink). They are also identifiable in and their relative placement lines up with the end credits art:
The cane as seen in s5e2 appears to share only a single rune with the s6e6 cane, and I'm honestly not very confident in that identification because the relative placement is wrong. In hindsight, I think it's a very similar but ultimately distinct rune. There is, however, a positive identification of another rune from the tower set:
Combining all three sets, there's the house exterior matte painting. The tower runes (green) are faithfully replicated on the near tower, and the far tower incorporates runes from both cane views (s6e6 in pink and s5e2 in cyan). There's also a small set of runes near the door that draw from both the tower and s5e2 cane sets:
Finally, there's the interior, in both its concept art (by Lillian Lai) and finalized appearance. There are runes visible on the rug, but the one in the final screen appearance doesn't match the concept.
You can also see the other reason I did all this work, which was to confirm whether the big "K" crest over the fireplace is a recurring rune or a unique piece of (presumably) heraldry. It's a rune: s5e2 cane rune #2, visible there, here, and in the exterior.
In the interest of exhaustive detail, there are also a couple runes on the floor in the map/dungeon room, but they do not correspond to any others as far as I can tell:
(Nor do any of these correspond to the carousel runes, just in case you were wondering. Or to the runes in Puzzle House, but that part isn't very surprising.)