Do I need a consent banner for Housing Market Publisher?
Yes. Show your visitors a consent banner, your own or the small built-in one. The script sets no identifier until a visitor agrees, and in some countries no ad is shown until they agree to advertising.
Yes. You show your visitors a consent banner, either your own or the small built-in one. The Housing Market script does not set any identifier on a visitor until they have agreed.
In some countries, for example in the EU and the UK, no ad is shown at all until the visitor has agreed to advertising. In those countries a visitor who has not agreed sees no ad, and the slot disappears.
The publisher terms you accepted in the Publisher app say what is expected of your website. What the law requires in your country is for you and your own adviser to decide; this answer is practical guidance only.