Okay, I found the issue. I had the power and ground connected to the large breadboard (with the LEDs) and then to the small breadboard with the ICs. I connected it to the small board now and voila: problem solved.
Total oversight, I don't know why I connected it from the large to the small one.
Yeah that made absolutely no sense. I was trying to explain to my kid that it makes current flow only one way, and then I left it there for no good reason.
Currently stuffing a sock into my mouth to stop myself ranting about using Unos/Megas with breadboards, flying connection wires, those plastic/wood carrier boards with an Arduino nailed to one side and a breadboard nailed to the other side... this is what gives breadboards an undeserved bad reputation... oh sorry, the sock fell out!
This is how I like to wire breadboards. It's not a perfect technique, but at least you can see how everything is connected. You have a reasonable chance of spotting a mistake and fixing it.
Wires can be much shorter than those 'jumpers' without laying them flat / perfectly spaced. Breadboard wiring I do with stripped wires (#22), save those for re-use. Arduino to breadboard I use 'jumpers', with the crimped terminal (not the round wire / handle sort).
Interesting. So not entirely dissimilar to the so-called "Dupont" pins. (Makes me wonder how they accumulated that name - "Dupont" - as AFAIK, a plastics producer but not a component manufacturer.)
And I thought the "handles" were cast on, not just slipped on.
Lucky then, many now sold are aluminium - cannot be cut short and soldered.
I'd hazard a guess that they're slipped on with some glue - certainly not cast anyway.
There seem to be different types, the one with the sleeve off came from the official (I guess) Arduino Starter Kit, but I also have a Elecrow Starter Kit, and those have wires with a slightly different color. So I'm not sure if those are copper or aluminium.