Vegan cats is such a weird hill to die on for vegans. Mostly, because it isn't a hill. Hills give you tactical advantage. The position with the vegan cats is basically indefensible. I can't say for sure that it's impossible to feed cats a vegan diet that's healthy for them.
I've googled 'vegan cats' and the first thing I found was an article from the Guardian: https://www.theguardian.com/lifeandstyle/2023/sep/13/cats-may-get-health-benefits-from-vegan-diet-study-suggests. However, a problem I have with the article, and the study linked (https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0284132) is that the methodology was for the pet owners to report the cats health status. I feel that this doesn't produce a reliable result. The most important factor is that it's not a controlled environment. The cats may be allowed outside, which means that they would supplement their diet through hunting. My standard for evidence is a study were the cats are fed a vegan diet in a controlled setting.
The fifth result, a site called Vegan Outreach (https://veganoutreach.org/vegan-diets-cats/) seems to provide a nuanced take, I skimmed the article, and their conclusion says that more research is needed. They mention another study which tested two vegan diets for cats found them lacking in key nutrients.
The position with the vegan cats is basically indefensible.
What do all organisms, including animals, need to properly maintain their metabolism?
Nutrients.
What are nutrients?
A bunch of different chemicals.
Depending on the specific organism, another set of nutrients is required, also varying in amount of course.
All required nutrients for humans at least can be obtained or synthesized from non-animal compounds.
From that simplified perspective, it's absolutely rational to explore how we could feed animals like cats on a purely vegan diet.
But it's certainly nothing which should be left to do for the layman alone, as veterinarian care is advisable if harming the animal should be avoided.