As for him not wanting to accept Katarina energy, it is for practical reason.
It is not that he wants to sacrifice himself for her.
In the past, he would not hesitate to do so.
But Katarina and Sofia made him understand, that just because he sacrifices himself for them would not mean that it is the best choice.
Unless he had no other choice, unless he had no other measures, sacrificing himself for them is the last thing he would do. Because he knows how that would make them sad
Just like he couldn't accept it if either Katarina or Sofia sacrifice their life for him. That would burden him for his entire existence.
That is not a burden he wanted.
The particular reason he did not accept Katarina energy is simply because if he managed to break the suction force that is pulling him and Katarina toward the eye, then Katarina who still had energy could bring them to the portal and exit this time space tunnel