>> "Most new homebuyers will pay around 30% of their income on their mortgage"
You go to the bank looking for a loan. They use that exact sentence to determine your monthly payment. Lower interest rates mean you can borrow more for a given payment. Then they tell you how much you can borrow. Everyone involved - banker, agents, seller, neighbors - wants you to spend as much as possible. Even if you don't, prices are set by "the market" where people do. Hence prices are determined by interest rates.
That first statement has been fairly constant for a very long time.
There are exceptions in areas where other factors distort the market.