This matches many parts of Too Like the Lightning by Ada Palmer, first book of the Terra Ignota series. First book published in 2016.
- One faction (the Gordians) has a method of psychological (not genetic) classification using a series of numbers.
- The world is linked by a ubiquitous transportation system of flying cars, so fast that national borders are meaningless.
- Two of the characters (Ganymede and his sister Danae) isare engineered to be beautiful and charismatic.
- The car transportation system is largely run by 2 siblings (Eureka Weeksbooth, and I forget the other name). They are not genetically modified, but have been psychologically trained (some would say mutilated) since birth to repurpose all their senses for data input.
Semi-matching: One faction (Utopia) have a city on the Moon and are working on terraforming Mars, and are the most technologically advanced. Some people revere them and their creations.
Non-matching: major services aren't really owned by families led by genetically modified people. Also, the plot doesn't really center around the people modified to be highly charismatic and beautiful.