Do I need a website for Google Ads, or is the listing enough?

No, if the listing has hours, a photo, a map and a call button someone picks up. You need a page when the offer does not fit there: a long menu, groups or an appointment with conditions. Open the listing on the phone and try to book without leaving it. If you can, the ad lands there; if you cannot, the page is the destination. A site is built “so we can advertise” and the click lands on text with no phone. The listing already had it and was not used. The destination decided: a complete listing or a page with the same phone and the same hours. The ad is not switched on against a half-built site.