I’m an electrical engineer living in Los Angeles, CA.

You’ve got the important foundational elements. The other big event is the Horus Heresy, where about half of the Emperor’s sons fell to Chaos and started a huge civil war that left the Emperor in his current half-dead state, but the imperial bureaucracy keeps on chugging.
The other thing to keep in mind is that the world of Warhammer 40k has been evolving over decades of novels, tabletop games, and video games made by multiple authors. As a result, the canon is vast and occasionally self-contradictory.
If you want to know more, I highly recommend the Ciaphas Cain books (novels with a comedy streak) and a silly fan series called If the Emperor Had a Text-to-Speech device.

You’re confusing PEGI (the European games rating body) with ESRB (the American equivalent).
PEGI has ratings 3, 7, 12, 16, and 18, and it gave Balatro the highest rating of 18.
ESRB has ratings E, E10+, T, M, and A, and it gave Balatro the relatively low E10+ rating.
In short, there’s increasing hints that the “greater good” espoused by the Ethereals (i.e., the Tau’s mysterious leadership caste) may actually be a cover for a lot of mind control and eugenics.