A business can sell "goods" (/"products") and "services".
Is there a term that encompasses both of these?
Various words may fit (e.g. "offering"), but I'm looking for the technical term, if there is one.
I'm not aware of any such "technical" term in economics. Goods and services are referred to as goods and services in economics, period. From the example you give in the comments, it looks like you're trying to write an introduction/review of a business. In that case, not using a technical jargon, be it existing or not, would probably be better anyways. By the way, X = "offering" sounds pretty good to me.
The trouble with economics is that many of its technical terms either have broader or narrower meaning in ordinary language. "Good" is one such example. A good is any thing that can be used to satisfy a human want, provided that the person who wants to use this good can (i) control it, and (ii) believes that she can use it to satisfy her wants. This is a much broader definition and narrower definition than the ordinary language definition. But this is the technical term that you are looking for (see also Giffen good, club good, public good etc.). Although, an economic good would perhaps be more precise (i.e. if a business produces it, then it's probably not available in abundance. In other words: it's scarce. It's something to economize.).