Rent stayed flat because of the moratorium, not because of the demand. You will start seeing the rent increase as the leases are coming up for renewal, many places are already up for 20% rent increase.

House prices are roughly dependent on income which means dependent on monthly payments.

Rents are even MORE dependent on income and it’s easier for renters to move, so rents often end up below the mortgage cost for a similar purchase.

Take a fixed monthly payment, with lower rates the principal can go up. Thus house prices can go up. On other hand renters have the same pretty much fixed monthly payment.

Rent's are not tied directly to value of property, but need to service the debt linked to property. Or equivalent one.

sokoloff was talking about rising rates, not rising rents. And I agree completely, when interest rates rise money is more expensive, thus credit/mortgage has more interest, thus people can’t afford that much of a property price for the same monthly installment, thus property prices are going down.