How much ozone is required for water purification?

It depends on the water source, and the contaminants in it. Spring water or RO water is dropped into bottles with 0.2 to 0.4 ppm of ozone. This just keeps the contents "sterile" until the bottle is capped, and the ozone decays back to oxygen.

One community in California gets their drinking water from an underground well located in a buried ancient redwood forest... and ozone cannot treat it economically. The low tens of ppm of ozone were applied, and eventually so much oxygen ended up in the water, the carbon filters would get bound up with all the gas. To say nothing about corrosion in the distribution system from high dissolved oxygen.

Ozone doses of 1 - 3 ppm are ideal (cost and payback), and other treatment methods need to be applied either before or after ozonation (adding ozone to water), to allow this much / little ozone in most surface water sources.

Underground sources commonly only require filtration and/or ion exchange. Ozone is not usually required unless the ions are not fully oxidized, which is why they are found dissolved in water. Examples are iron, arsenic, and manganese. Manganese is a tricky one. Within increasing oxidation it goes from soluble (bad), to insoluble (good, can be adsorbed to something), to soluble again (bad). So ozone doses here have to be carefully applied.