I don't know about the other appearances of the cat, it could just be slipping, as other animals do. But the fact that the cat is associated with Maya, and Makoto heavily presents a Maya agenda before mysteriously disappearing might be related. Her words to Akira herald the spring which makes him calm and receptive to the idea of doing exactly what many of the gods want. Also, Makoto finishing with "I love you so much" is a repeated pattern of someone else, and quite supernatural at that.
I want to second this and add:
Maya is also known as the "Stray Cat".
And Makoto is pretty much discribing Maya's existence/situation of being trapped in the cycles for who knows how long and being an adult (actually an elderly woman
) trapped inside a teenage body.
So i guess the cat is supposed to hint at that, at least in that scene.
at all:
I didn't get any NTR vibes from Tsubasas event/s /pictures, was still strange though, because it was shown.
I mean whats in the past, stays there.
What i found more interesting, while she tried to keep it a bit in the shadows if it actually happened, and i think she did because she wanted to keep her and Akiras power dynamic intact, it did happen.
And how she called it a family tradition and, iirc a ritual, it shoves her and her family it bit further into the cultist direction.
Would also explain why shes pushing her daughters onto Akira.
To conclude said tradition/ritual.
And her "old friend" could also be Sekai, while that was already mentioned here afair.
Not only a friend but a family member, maybe from a different family branch, a sub branch?
And Sekai cut ties with her whole family before or after she had to undergo said tradition/ritual?
Kinda gives me some Rize vibes there.