The "right" amount of risk is subjective. You are correct that a person's income, assets, and liabilities contribute to the capacity to take risk. Some people are also more comfortable taking risk than others.
Time horizon is also important. Some investments cannot be sold quickly, but might have higher expected returns to compensate. Some university endowments invested heavily in illiquid assets based on this belief. It worked well for awhile, but later struggled. See this article for more on this.
You may also want to consider an asset/liability framework. In this view, the present value of future expenses increases when interest rates decline.
You are correct that different types of equities and bonds have different amounts of risk. High yield bonds have a much different risk profile than treasury bonds. There are a number of ways to measure risk. You could look at the portfolio historical standard deviation or maximum draw-down as potential measures.
The "correct" allocation also depends on your comfort with complexity. For example, are you comfortable having a different allocation in your taxable account and retirement account? Are you willing to take the time to understand why the best portfolio might involve different assets in different accounts?
Health is also important. Some people feel like can work into their 80's while others lose the ability to work much younger. If you have the option to work, you have a higher capacity for risk.
As you can see, the inputs for the "right" answer can be both unique to the individual and subjective. The output isn't fully objective either.