Also note that 'according to' and 'in keeping with', both valid uses contextually of the preposition κατὰ can mean the same thing, but often don't. It can also mean, "unto", "toward" or "for" or "against (positionally)" or even "of".
The Greek is pretty plain in most cases, but to your two examples: (1 "He chose us according to His foreknowledge", which I suppose you take from 1 Peter 1:2 contextually, even in the same verse 2, shows choosing for a purpose —"...through the sanctifying work of the Spirit, to be obedient to Jesus Christ and sprinkled with his blood:" and (2
“for those whom He foreknew He predestined” (Romans 8:29) continues with "to be conformed to the image of his son." —purpose
(Haha looking for a different reference, I came on this, from bing: In Acts 2:23 God’s foreknowledge is explicitly causative: Jesus was “delivered over [to death] by the predestinating purpose and foreknowledge of God.” and this: "Also, if God’s choosing us were based on His foreknowledge that we would choose Him, then He really didn’t choose us at all. Rather, He only would have responded to our choosing Him by then choosing us. But this would make God’s plan of salvation depend on the choices of fallen sinners, rather than on His purpose and glory.")
In all cases, the principle acknowledged by Biblical philosophy concerning God, is that, since he is not bound to time, for him to foreknow something is for it to have happened already. Further, since all things come from him, whatever happened, happened by his causation. There is no other creator.