You seem to be talking about synthesis, described at Wikipedia as ‘a combination of two or more entities that together form something new’.
The term figures prominently in the classical philosophical process of dialectic, which hinges on the ideas of thesis (a proposition), antithesis (a challenge to that proposition) and synthesis (something new that emerges from discussing the two in a firmly reasoned way). Dialectic literally means something like ‘speaking through, or across’, and is about rationally connecting ideas that seem somehow antagonistic. Wikipedia again: ‘The outcome of such a dialectic might be the refutation of a relevant proposition, or of a synthesis, or a combination of the opposing assertions, or a qualitative improvement of the dialogue’.
That very precise sense of synthesis in the dialectical process is specifically about ideas that are regarded as being opposed, which in most daily life would probably be fairly extreme cases, but it shows the potentially ambitious scope of the idea. The term is also used, however, to talk more generally about combining any previously unconnected (intellectual) components to form a new system of some kind.
Accordingly, Merriam-Webster defines synthesis very broadly as ‘the combining of often diverse conceptions into a coherent whole; also, the complex so formed’. That seems to be very much the phenomenon that you describe: it can be formally aimed-for (as in a dialectic), or can emerge relatively accidentally, as in the example you give.
The negative connotation that you finally mention seemed jarring at first glance, since on the whole synthesis is generally regarded as a positive thing: something new and surprising has been created through combining existing elements in a novel way. The connotations tend to be positive ones, of discovery and creativity, so ‘telling my friend that his attempt to connect these two unrelated topics is not very impressive’ initially seemed a bit odd.
Then again, in simply thinking about the concept there is nothing to say that any given synthesis should be as successful, as useful or in some other sense as elegant or pleasing as any other synthesis. Presumably some such attempts can be naive or misguided, although the act of making such an attempt might still be thought laudable.