In ArcGIS Pro, individual symbol and style elements can be saved but there does not appear to be a tool for bulk "exporting" or "saving" of symbols. See help- https://pro.arcgis.com/en/pro-app/help/mapping/layer-properties/save-symbols-in-styles.htm
ArcMap has the “Export Map Styles” via customize > tools > export map style. This is very handy for exporting all symbols in a layer or map to a new style.
Something similar in ArcGIS Pro would be good.