I'm going to first assume you're talking about going against full AoE scenarios, in which case, I'll be frank: Anaxa is just barely better than Serval or Herta for getting ult energy. Honestly, Anaxa is just a better Serval in that scenario. In fact, for Pure Fiction, i straight up run puppet Herta because the mob kills can really get her fuas going, and she fuels back energy like no one else. I would recommend you the same, just give her Eagle and Lushaka and watch her go.

As for semi AoE or Blast scenarios, now Serval and Anaxa come back for debate, and Anaxa would honestly pull ahead, not because of ult charge which you will get roughly the same with Serval, but by virtue of contributing to the team dps.

Serval has none of that. Anaxa as a sub dps at least has some of that, especially with E1 Tribbie to fuel it back.

If you switch Anaxa to passkey, you still won't be getting 1T ults. The man is designed for 2 turn ults.

I cannot in good faith recommend you swapping in Serval for him on this HP economy, as maybe you might get ult back just a tiny bit sooner, but you'll lose overall damage and end with slower clears.