The main advantage of organic fertilizers is that they not only contain a balanced amount of nutrients that enter the soil as organic matter decomposes, but also significantly improve the physical properties of the soil.
Of course, neither ash, nor lime, nor dolomite flour can be considered organic fertilizers, since there is no organic matter in them. Organic compounds are not absorbed by plants, therefore the nutritional value of organic fertilizers is largely due to the activity of soil organisms that contribute to the mineralization of organics: bacteria, fungi, worms, etc. P.
You can hardly be considered organic fertilizer peat: the content of the nutrition elements in it is extremely small. At the same time, adding peat to the soil can change its physical properties and activate the activities of microorganisms living in the soil.