The original (and still core) sense of concern has its roots in Latin con = with and cernĕre = to separate (which also give us discern = distinguish, recognise with the dis = apart prefix).
That's to say, concern = pertain to, be about, relate to - effectively, OP's definition #2.
In fact, OP's initial definition superficial = not [concerned with anything] serious or important would seem perfectly adequate to me even with the [bracketed] portion removed entirely (it adds little extra meaning).
Outside of additional context, "This problem concerns me" could have several meanings, including...
it affects me - I have some kind of relationship to the problem
it's about me - I am central to the problem (but I may not care much anyway)
it's important to me - I care a lot (but may not be personally involved)
it worries me - I care a lot, and have reason to fear the eventual outcome may not be what I want
I hope that series of definitions gives some idea of how the meaning has become "stretched" over time.
The sentence "X is superficial" (from French superficiel = located at or on the surface) normally means...
X is shallow, frivolous - you won't find any "hidden depths" in X
X is only interested in outward appearances - X doesn't look for deeper meanings in anything
Thus although I said above that definition #2 applies for OP's purpose here, it's also possible to say that definitions #1 and #4 could apply...
superficial
1: not involving anything important
2: not about anything important
4: not interested in anything important
The one that hardly applies at all is #3. We wouldn't normally use "John is superficial" to mean John isn't anxious about, or upset by, important things (we'd say unflappable, nonchalant, even-tempered, etc.).
You missed the irony, actually.
All I felt was that Anne seemed to really like her guests, and she even wants to cook for them.
No, she does not. She hates them. She hates they are there. She hates her housemates for inviting them.
The whole conversation is expressing the opposite of what they really mean.
Typical example of irony:
O, isn't this lovely! -> meaning "this really sucks!"
Best Answer
According to the OED, byss is an obsolete word meaning the opposite of “abyss”. “A” is sometimes a prefix denoting negation. So I’m guessing Churchill means “infinite heights and infinite depths”. He’s being poetical, and comparing this to infinity and negative infinity.
It’s not a word you will ever see in normal speech or writing. It’s one of two words in that quote that I, as a well read native English speaker, have never, ever encountered.