Too bad that @IKEA is deliberately making it hard to
repair or enhance this lamp by using rivets to seal the enclosure. I have to
drill into 20 of them to open up the lamp.

Removing them ...

Here it is. 4 panels with 4 sct2024cssg doe00566 ICs each and the first panel
where the power and buttons are connected has a GODX1S2 KL2209.

The GODX1S2 seems like a custom IC.

... that controls the 16 SCT2024 (which each have 16 channels), so this means a
total of 256 LEDs.