Organic is a co-opted term in US and one where producers have to pay to use it both for land certification and produce/meat certification. Compliance is a lot of bureaucratic paperwork. Recycling manures in composts is fine.... though not absolutely essential for nutrient cycling. Horse manures in particular can be problematic because horses are given so many drugs. Regardless, as this other blog https://lachefnet.wordpress.com/2020/12/28/restoring-the-soil-microbiome/ from the same source notes, in regenerative systems, the key for plant nutrition is soil health full of active microbiology. Tillage, especially frequent tillage, doesn't promote soil health. Most organic relies on a lot of tillage.