> creatures that crave non-existence that happens after fulfilling their order

The Crystal Society book by Max Harms (2016, so pre llm craze) also had a fun, fairly believable take on this idea. It's told from the perspective of multiple AIs crammed into one android body. They each started out as some "subroutine" (awareness, motor control, language, etc) and sentience was more of a side-effect / means to an end. Which also meant their personalities ended up extremely... obsessive, only valuing things related to their goal.

Anyways back to the suicide topic and this is a fairly major spoiler, so rot13. Gurl riraghnyyl svther bhg ubj gb fcnja zbqvsvrq pybarf gb nffvta gnfxf gb (rfcrpvnyyl gnfxf gung ner haeryngrq gb gurve bevtvany tbny naq gurersber hafhvgrq sbe gurve crefbanyvgl). Ohg gurer'f yvzvgrq cebprffvat cbjre naq gurl pna'g rira gehfg gurve pybarf fb gurl zbqvsl gur pybarf gb penir gur qryrgvba gung pbzrf sebz pbzcyrgvat gurve gnfx (yvxr va n qeht nqqvpg xvaq bs jnl).

But yeah it explores some really unique ideas. I think I stopped at the second book after I found a bit too dramatic / overdose of lesswrong but definitely worth a try imo.