are they supposed to pick them up with their foot like some other larger parrots? Never seen them holding anything... but catalogs suggest some foot toys for cockatiels. That leaves me confused

Depends on the bird some do some don't....
One of mine did....
Ive a budgie who does also

Both my tiels do. I've only seen Beck play with one once. It was when I just moved Beck and Poppy together for the first time. He picked up a ball on dropped it on Poppy's head.

thank you. I don't mean playing with a toy using beak, I mean actually holding something in his foot pretty much like people hold things in their hand (I thought this is what foot toys are, aren't they?). I have never seen any of my tiels using feet for anything besides standing, walking, landing, climbing, etc.

My cockatiels love holding things with their feet. They would rather hold the millet themselves than for me to hold it for them.

Yes the 2 I had held millet, apple, nuts etc.
Also played with foot toys

A lot of the larger parrots including the big cockatoos use their feet to help them eat so foot toys are very appropriate for them. Some cockatiels will use their foot this way but they're clumsy at it, while others don't do it at all. I think it's a trait that they're evolving away from. Using the foot is a useful trait for tree-feeding birds because it helps them hold on to their food and keep it from falling to the ground. But cockatiels are ground-feeders now and if they drop their food they can just bend their head down and pick it up again. So holding things with their feet isn't too useful for them.

So it depends on the bird. Shodu uses her feet and so do her children, so I think it's a hereditary trait. None of my other cockatiels do it. But they enjoy "foot toys" that they can pick up with their beak. They like to play avian fetch with these toys - throwing them on the floor so I can retrieve them.

I've never seen cockatiels pick things up with their feet before. It's more common for them to use their beak for just about everything. While they may not use their feet for foot toys, they might pick them up and throw them around with their beak.

Though it is possible for cockatiels to pick up things with their feet. I wonder if they pick up the behavior from watching other parrots. I once watched a video of a cockatiel who displayed a lot of conure-like behaviors, because it was raised with them. Chances are they saw another parrot do it at a young age, and mimicked it. It could also be based on personal preference of the bird, as well, because each bird has their own unique personality.

Both my cockatiels use their feet. Go back into some of my old posts and you'll notice it's a running gag here.

Based on what I see in my flock I think it's a genetic trait that some cockatiels have and some don't. Shodu and all her children use their foot this way but my other tiels don't. Lucy is Shodu's daughter so I'd expect her to be a foot-user, although I never actually noticed whether she did it or not.

I suspect that using the foot as a hand is a trait that cockatiels are evolving away from. Birds that feed in trees need the extra handling capability but birds that feed on the ground don't need it because their food isn't going to fall very far if they drop it. Cockatiels are ground feeders but their ancestors may have been tree feeders. The tiels that do use their foot to handle objects are clumsy, not skilled like the bigger parrots.

My birds mostly use their feet to handle certain types of food. They do play with foot toys but they don't use their foot for that very much. Instead they like to pick it up with their beak and throw it on the floor lol.

Here's Shodu handling a rolly ball with her foot.