In the USA, are there popular rent / spending / saving ratio recommendations?
I would say "No", there is not a popular ratios governing personal finance categories. Really it is very dependent upon your goals and stage in life.
For example, people who embrace "FIRE", or financial independence, suggest saving between 50-75% of their income.
When people are young 30% of their income for housing is pretty common as their incomes tend to be lower. Young people tend to buy homes pretty close to the top of their budget, but as they age their income tends to rise while their payment remains pretty close to the the same. After 20 years of raises and promotions, their housing costs tends to be a lot less of a percentage of income.
For those who concentrate on being debt free, spending 1/3 of their income would be suicide to their plans, and should try to keep that around 5 to 10% of their income.
For housing 30% of income is pretty close to the max, some banks went as high as 40% in lending for mortgages, but more importantly they tend to measure your debt to income ratio. A person with high car payments and CC debt is more likely to default on a mortgage than a person who is consumer debt free.
For retirement savings, most authors agree that 15% is the right number to have a decent retirement. Statistics show that people tend to do this and more, or close to nothing. The deviation in average retirement savings is very high. This suggest that there is no "popular ratios" in the US.