The study mentioned here indicates otherwise https://www.tuck.com/the-inequality-of-sleep/

"the likelihood of short sleep increased with greater poverty"

Poor people are much more likely to work irregular shifts and night shifts, which have a serious impact on sleep.

And more importantly, even if the wealthy get less sleep, that's by their choice, not circumstance. A poor person loses sleep because they have 2 jobs and the shifts don't line up. A rich person loses sleep because they've taken on too much to do of their own volition, any amount of which they could abstain from with little consequence.

It’s more complicated than that: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2861987/

Your study supports my point and harms yours. From your study:

Lower income and educational attainment was associated with more sleep complaints. Employment was associated with less sleep complaints and unemployment with more.

Rates of sleep complaints in African-American, Hispanic/Latino and Asian/Other groups were similar to Whites. Lower socioeconomic status was associated with higher rates of sleep complaint.