One of the best enrichments for hands-off birds is simply giving them new things to interact with.
The vast majority of hands-off birds are this way because they’re fearful. To get them to gain confidence, you have to teach them that not everything is going to kill them, and interacting with new things can be rewarding! The most people have with this is they go too fast, you need to start small and advance at the pace your bird is comfortable with.
Before Bjorn and Ursula were in my care, they never had change. They had the same flock, enclosure, food, perches, everything; their life was static. Suddenly everything was turned upside down and they were shoved in a box and thrown into a scary place with birds they’ve never seen and surfaces they’ve never stood on!! This made them extremely fearful, because they simply did not know how to react to new things. So I had to give them space for a while and let them settle down.
Now that they are starting to relax around me and even eating out of my hands, I need to get them confident to get them to progress further. I do this by putting new objects in their enclosure. Nothing too scary, start by putting things they can see outside of their enclosure everyday. For example, there’s a useless little brick that just chills outside the yard barn. It’s small, about the size of my hand, barely big enough to perch on. All I did was put it in their cage without anything to entice them to begin with. This was easy for them, Ursula responded positively and was down with this brick right away! She hopped on it and called Bjorn so they could both spin in circles and coo on the fun new texture.
Next step is something a little more scary, a rock. These birds are used to polygonal shapes so a round, lumpy rock was WEIRD. Luckily the stone brick helped them get used to the texture, so once they got passed the stretching their necks out and turning their head every which way stage, the coolness didn’t freak them out too much. Pigeons really enjoy having unique things to stand on, so I still wasn’t using treats to entice them at this point.
After I’ve given them multiple rocks to interact with with varying size and color, I’m going to move onto an earthly-colored cloth on a rock. Then I can try putting in bright colored cloths to help them be okay with any clothes someone might wear that would be bright. Eventually I’ll move onto something like say, a metal spoon, and put treats in it to encourage them to interact with it. This will help lead up to enrichment toys that they have to work to get the food out.
It’s really important to put yourself in your bird’s shoes, er, feathers. Think of all the things that are completely normal to you, but are new and foreign to them. Don’t be like “but it’s just a cup! How can you be afraid of a cup” because how are they supposed to know? Try to think of when you were little, maybe you went to the zoo and saw an animal like a sloth you’ve never seen before. It might’ve freaked you out! Maybe your parents had to calm you down and insist that it was fine. But with birds that don’t know they can trust us, we can’t do that, we have to let them figure it out themselves. Be mindful that a hands-off bird will typically be happier and more confident with a feathered friend that they know and love- it’s safer in numbers.