The energy point number on the badge is for what you get when you earn them. The italicized descriptions under their names tell you how to get them.

How do u get the black hole badges, Atlas, Artemis and Tesla? I'm not sure if it's energy points or something else.

This post was marked as "pending approval" and the approval process takes forever so I'll try again to post this with some padding text so that it can hopefully go through.

To earn Atlas, you need to master 5000 skills.
To earn Artemis, you need to master 7500 skills. (Only 3 known people have ever done this.)
To earn Tesla, you need to earn 10 million energy points.

So, Artemis is near impossible, technically?

Somehow, there's no Da Vinci badge in my not owned badges (I made up the not owned).

Yeah, Artemis is nearly impossible in that it takes well over a year, if not multiple years, of consistent grinding to earn it.

The Da Vinci badge was retired for no reason back in 2020.

In 2020, a number of badges were retired because KA was modernizing its codebase.  They moved from Python 2 to Go.  That change made the previous badge system more costly and more difficult to maintain.

Around that time, KA also did away with the "Mission" system, in favor of the "Mastery" system.  This meant that achievements were calculated and acknowledged in a different way.

Either way, badges were not discontinued "for no reason."

This one in particular was removed for no reason. They implemented the lower and higher mastery badges (which are over 10 times more expensive to compute), so there was no reason not to implement Da Vinci.