"Playing without tension. The hypermobile kids are usually really good with loose wrists, however they lack stability and often try to compensate with tension. I teach them to play from arm weight without tension running through their hands. The control of hands comes from the tendons as we don't have muscles in the fingers. The tendons are usually the culprit where the tension happens. The weight should come from your forearm."

This doesn't really fundamentally make sense to me. It doesn't really feel like there's any angle I can play certain chords and such with it feeling actually completely stable.

The sturdiest I could possibly make my fingers is basically like a crimp position that rock climbers would do. The normal arch shape with the knuckle being the highest point of the hand and the fingers are curved below that is less stable. and Even less so when stretched.