Both your statements are mostly correct, with some nuances:
Your first statement list is missing something:
Specifically, it is missing a numenera plan (Numenera Destiny, p. 135). Those are the numenera assembly instructions, and you cannot craft numenera without them. Problem is: Plans do not come easily. And, unless your character get access to numenera plans through advancements (Wrights, mostly), you do not decide which plans you get.
On the bright side, if you can craft an artifact this way, you can do it again as long as you can gather the necessary resources.
Your second statement is only correct sometimes:
From Numenera Discovery, p. 127:
If the item is fairly simple, the GM can skip the crafting details and
just say that after a period of time, the PC creates it. For an item
that significantly alters gameplay [...] the GM might require difficult
rolls, a considerable amount of time, and rare, hard-to-find
components and materials.
So basically, with XP you choose which artifact you want and you may skip some or all of the other requirements.
The bad part is that you only get the artifact once. And since many artifacts are in no way permanent (that depletion dice...), your non-refundable long-term XP expenditure is just a bad roll away from becoming a short-term one.