More likely is they will grow more slowly rather than anything
Don’t expect anything near pre-covid prices anytime soon for the principal
Raising the interest rates makes homes more expensive over the lifetime of the loan inclusive of interest. It does not however increase the principal cost of the home in fact it has the reverse effect.
People often budget the size of their loan based on the monthly payments. When interest rates go up, payments go up, size of loan goes down. Smaller size loan effectively lowers demand. Lower demand, home prices fall (or just rise slower).