What is せっかい焼き and how does this sentence work?

Question

A and B have been talking, discussing politics, policy and like. Since A is CONSIDERABLY younger than B, B has been more advising A on things as they talked. Then this bit of conversation happens:

A: ありがとうB(. )少し…見えた気がする

B: なに

A?: お前よりは長く存在している者のせっかい焼きだ

This is my current understanding of the bit, with the caveat that the last one is HIGHLY problematic.

A: Thank you B. I felt... I saw (it) for a bit.

B: What?

A?: Meddlesome person who existed longer than you did.

Last line is literally (as far as I can see):

A?: Than you (toppic) nosy 焼き longer existing person, it's.

If this is A talking (which it might not be, since this manga doesn't use bubble arrows) which makes most sense given the exchange, it seems she is talking of someone older than B. But let me tell you there isn't anyone older than her that is relevant.

This could be B talking, then the age bit does make sense and omae is A, BUT, in the previous section it was B who was providing advice and guiding A to conclusions, so it's not that either.

The only thing I could think of, it's some fancy way to refer to what B was, since she did change recently and there was some memory loss. Also B has been linked with fire quite a lot, so 焼き might be a reference to that.

And yeah, I am not sure what せっかい焼き means, although I'm pretty confident せっかい is probably nosy or meddlesome.

So question 1: is the meaning of せっかい焼き Question 2: is how would one interpret the last line by A?.

Answer 1

節介{せっかい} in this sense (often but not always rendered as おせっかい) is closely related to (お)世話{せわ}, and both of them are commonly paired with the verb 焼く. To (お)世話を焼く is essentially to go out of your way to help someone out. To (お)節介を焼く is pretty much the same thing, but with a bit more emphasis on the fact that you're providing help that wasn't asked for.

By extension, the nominalised form 節介焼き can refer either to a person who's always trying to offer help that people didn't ask for, or to the act of offering that help. In this case, it's the latter - the せっかい焼き B is referring to is all the helpful advice they've just been offering. Calling it せっかい is a form of classic Japanese humility, since they're framing the helpful advice as something they offered for their own self-satisfaction and therefore not something A needs to thank them for.

I'd translate the whole exchange loosely as something like:

A: ありがとうB(. )少し…見えた気がする
Thanks, B. I think...I'm starting to see things a bit more clearly.

B: なに
B: Don't mention it.

B: お前よりは長く存在している者のせっかい焼きだ
B: Just think of it as a bit of unsolicited advice from someone who's been around longer than you.

By the way, you'll find this sense of 焼く listed as meaning 8 in the デジタル大辞泉 entry:

８　あれこれ気を使う。扱いなどで悩む。「世話を―・く」「手を―・く」

It's a very particular sense, though, that only really occurs in a small handful of collocations.