While you are welcome to your take, sometimes a cigar is just a cigar, and here's the writer/director responding to that very scene:

Li: Speaking of those video clips, let’s talk more about the ending. Can you tell me about the decision to have the Barbies and Kens reach, not a definitive solution, but kind of a détente? President Barbie, played by Issa Rae, does not allow Ken a seat on the Supreme Court. They’re still figuring things out.

Gerwig: We’re all still figuring things out—that’s part of it. But the only thing I could ever give anyone is that they’re all still in the mess. Maybe it’s a little better for the Kens. You don’t want to tell people how to watch things, but at the end of the movie, the production design incorporates some of Ken’s fascinations into Barbie Land. Like, the perfection is not as beautiful as the thing that started blending everything together. I remember when we went to shoot the finale, when we all walked on set, we were like, This is the most beautiful it’s ever been.

• Greta Gerwig’s Lessons From Barbie Land