>There are deposits of these rare earth minerals elsewhere. There are always more deposits, it’s just that they’re untapped until we deplete our cheaper sources. If China withholds its minerals, we will use more expensive sources, but we will still get the minerals.

Same thing if you with-hold semiconductors. Somebody for sure is willing to sell general purpose chips to China second hand at a more expensive price.

>I am less convinced that China is really good at playing the long game, and more convinced that China is subject to many of the same political struggles that we see in the US.

Unlikely. China is subject to different struggles but they are much better at playing a long game given that their power is more centralized and has longer terms. Xi Jing ping is likely here to stay. Bidens term is almost up and the next guy may just undo everything he did.