Not true. "Disposable" vapes use commodity li-ion cells, of the same basic type that you'd find in a cellphone, a laptop or an EV. They probably aren't the best quality, but there's nothing unusual about the chemistry or packaging. Li-ion cells are the preferred chemistry because of the very high discharge rate - alkaline or primary lithium cells just can't deliver enough current. The cell is perfectly capable of being recharged, but some people prefer the convenience of a disposable device and manufacturers are quite happy to respond to that demand.
It's wasteful, I don't particularly approve of it, I expect to see a lot of jurisdiction ban disposable vapes, but nor do I think it's particularly egregious or meaningfully impacting on the commodity price of lithium carbonate.
https://hackaday.com/2022/05/05/2022-hackaday-prize-disposab...