Apple Aperture with new Mac OS such as Ventura and/or Sonoma?

Unfortunately it's not doable. Aperture was dropped along with iPhoto several years ago. So you'll have to use Photos or one of the other image management apps.

You can import your Aperture photos into a Photos library via the Import menu in Photos. However, if you have a lot of organizational effort in the Aperture library, i.e. folders, albums, etc., you might want to consider using the paid version of PowerPhotos as it is more thorough in importing into Photos. A user tip shows the differences between the two is here: Merging/Importing iPhoto/Photos library into Another Photos Library: PowerPhotos vs Photos… Or not.

Apple is out of the advanced image management business. All they are offering now is the free Photos app, which, imo, is considerable much more advised that iTunes ever was.

You might want to stick with Lightroom and DXO.