Meaning of "concern" in context

Question

This is the definition of superficial from OALD:

not concerned with anything serious or important and lacking any depth of understanding or feeling

What does concerned with mean here? There are four senses of concern from OALD I find that all seems to be appropriate to the context:

1 [often passive] concern somebody/something to affect somebody/something; to involve somebody/something
- Don't interfere in what doesn't concern you.
- The loss was a tragedy for all concerned (= all those affected by it).
- Where our children's education is concerned, no compromise is acceptable.
- The individuals concerned have some explaining to do.
- To whom it may concern … (= used for example, at the beginning of a public notice or of a job reference about somebody's character and ability)
- Everyone who was directly concerned in (= had some responsibility for) the incident has now resigned.
- Please pay attention because this information concerns all of you..

2 concern something (also be concerned with something) to be about something
- The story concerns the prince's efforts to rescue Pamina.
- The book is primarily concerned with Soviet-American relations during the Cold War.
- This chapter concerns itself with the historical background.
- One major difference between these computers concerns the way in which they store information.

3 worried and feeling concern about something
- Concerned parents held a meeting.
- concerned about/for something The President is deeply concerned about this issue.
- concerned for something He didn't seem in the least concerned for her safety.
- concerned (that)… She was concerned that she might miss the turning and get lost.

4 concerned (about/with something) interested in something
- They were more concerned with how the other women had dressed than with what the speaker was saying.

Answer 1

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.).