This story does a good job of bringing to life how hard it is to find a Section 8 apartment in LA, but it misses the big picture.
"Inflation has caused rents to soar across California" is a tautology - rising rents are inflation. Housing shortage is the cause of the rent inflation.
https://www.nytimes.com/2023/02/17/us/housing-voucher-search-los-angeles.html
Housing Search With a Voucher Is Difficult in Los Angeles County

As the housing crisis deepens in Los Angeles County, one young woman learns that searching for a place of her own is more difficult than ever.

I'd argue the software company coordinating a price fixing ring among corporate landlords had a significant effect on rent inflation, enhanced by shortages caused by price speculation by those same landlords.