I'm not aware of any documentation that discusses migrating from the classic to the new map viewer. This blog post is the most I could find. https://resource.esriuk.com/blog/moving-on-from-arcgis-map-viewer-classic/
But as far as migrating, technically, any web maps that are created in classic are already created in the new map viewer. You can choose to open your existing maps in either classic or new map viewer. They shouldn't have to be "recreated." Theoretically, they should just "work" in the new map viewer.
With that being said, one of the things that I've found that doesn't just "work" are relationship classes. In the classic map viewer, relationship classes are automatically inherited from the feature service and viewable in the pop-ups. That is not the case in the new map viewer, and those relationships have to be manually defined to be viewable in the pop-ups. And in your case, I'm sure there are other things that are different, like symbology. But unfortunately, I'm not aware of any documentation that lists things that are "different" in the new map viewer that have to be manually changed from the classic map viewer. I think at a minimum, all maps will need to be reviewed in the new web map viewer to ensure they are working as intended.
