There are a number of improvements that can be made to the UX - mabe these should be splitted up but here they are.
Ability to work on a variant with relations and publishing without the UX forcing you to view the whole baseproduct and all other variants - the current UX makes it easy to make misstakes.
Be able to create and add baseproducts and variants direct into selected product category - to make it easier to work with insted of first creation of the product and then connecting it to a category.
When you search for a variant article number the UX give you the baseproduct as a result - let the UX display both variant articlenumber that was found and the "related" base product.
When working on a variant never switch to baseproduct in the UX - let this be a choise for the user - if the user want to work with the baseproduct - just select it in the current dropdown under first tab.
Export of a filtered list - only include the matching variants into the export file - current UX export include all variants under the matching variant baseproduct(s). The front end / website do it correctly.
Enable configuration of how the UX category left menu to display connected base products or even the variants in the left menu tree / Category tree - this would make the UX faster for compines/brand who work with variants as core products.