It is not easy to specify exactly what does and what does not constitute an economic problem. Some people like to say that “economics is what economists do”, which tells you only that it is not completely clear what the boundaries of economics are. A traditional definition is that “economics is about the allocation of scarce resources that have alternative uses” or that “economics is concerned with human behavior in the ordinary business of life and the societal implications of such behavior”. I find all of these useful but still somewhat unsatisfying.
Instead of this, or in addition, I would recommend that you look at the Journal of Economic Literature classification codes (JEL codes). When researchers write a journal article they typically specify the JEL codes that best describe the topic of that article. I think that these JEL codes, while also of course imperfect, nicely reveal the breadth of topics that are all covered by what we call “economics”. I recommend that you browse these JEL codes for a while to realize this. One could for instance work on how to best teach certain subjects to undergraduate students (A22), the history of Marxist economic thought (B14), the econometric theory of hypothesis testing (C12), time series models (C32), the designing of field experiments (C93), household saving (D14), the theory of firm behavior (D21), the distribution of wealth (D31), how to run auctions (D44), how to design a market for kidneys for transplants (D47), philanthropy (D64), how to write contracts (D86), unemployment (E24), business cycles (E32), central bank policy (E58), trade policy (F13), migration (F22), macroeconomic issues of the euro zone (F45), portfolio choice (G11), public good provision (H41), and many many many other things.
My point with this is that economics covers probably a lot more than most people would have expected.
Here is the corresponding video (in German):