Check https://www.greencarreports.com/news/1099009_bmw-water-injection-can-boost-power-and-cut-fuel-consumption . Aquatune also dissociates water using electrolysis, which may potentially help some more although I would have thought that @ about 50% efficiency, they are using much more energy to create the H2 than what they are getting back in terms if improved engine efficiency.
I have made and installed water injection systems on a couple of vehicles and both responded very well. The water vapour removed carbon in the combustion chambers of one and prevented a major running-on problem it had had for years.
Lower octane fuel typically contains more energy than higher octane. It follows, that if water injection enables the use of lower octane fuel you are going to get better mileage.