I skimmed the article and it looks like they only look at water consumption within a city, but not in the broader region? In many parts of the US (eg. california), the city itself might have a limited amount of water allocated to it, and within that pool the rich might be exacerbating the crisis by filling up swimming pools or whatever, but when factoring in agriculture their consumption is still a drop in the bucket. The first source I found says that in california agriculture is responsible for 4x the water usage compared to urban[1]. It seems strange that the study omits this. I understand that the study is a case study on cape town, and maybe this dynamic doesn't exist there, but it's irresponsible to lead with a sweeping statement of "Urban water crises driven..." as if this is a factor among urban water crises as a whole.
Your concern is spot on, and it's not even specific to California. Nevada and Arizona also consume far more water with farming than all urban uses combined. Cutting back on swimming pools or lawns or whatever is fine, but it's literally a rounding error compared to the water consumed by farming. Nothing else will matter if we keep growing water intensive crops in the desert.
The paper is not so much a study as it is a de-growth position paper that will be used by other de-growth nut jobs to cross cite one another and make themselves appear relevant.
"Critical social sciences explain that these patterns are generated by distinctive political–economic systems that seek capital accumulation and perpetual growth to the exclusive benefit of a privileged minority"
"To conclude, theories on degrowth suggest that the only way to counteract the unsustainable and unjust patterns of elites is by reimagining a society in which elitist overconsumption at the expense of other citizens or the environment is not tolerated"
I only skimmed it too, but it seemed to only concentrate on Cape Town, South Africa, and as such didn't seem to be relevant to other places at all: the problems they described seemed to be local in nature only.
As you and the other responder note, the water problems in the western US states are entirely different, and largely because of agriculture. However, even if you just focus on swimming pools and green lawns in the desert, in western US states like AZ and NV, those aren't the "elites"; it's the middle-class people wasting water on that stuff.
[1] https://cwc.ca.gov/-/media/CWC-Website/Files/Documents/2019/...