I can only reply to your "impossible to detect" with respect to clusters with the "technically challenging but apparently real and prospects for better measurements and extension to larger scales is promising" at the end of Kaiser's 2018 slide deck https://chalonge-devega.fr/Kaiser_29mars2018.pdf which I do not think is contradicted by the (interesting, thank you!) Mpetha et al (2021) paper, which cites at least three of Kaiser's earlier publications.

Broadhurst & Scannapieco (2000) https://iopscience.iop.org/article/10.1086/312630 is also relevant here, as it distinguishes between X-Ray studies and optical ones (SPIDERS being an example of the latter) pointedly at §4.2.

I do not disagree that ~ 10-20 km/s is small, but it's the little things that cause "tension" headaches, isn't it?