We live in an apartment with 2 toddlers (1 & 2yo) and sometimes they run and stomp. I always stop them quickly, knowing we have downstairs neighbours. They recently knocked on our door asking us to keep it down as they have a 2 month old baby and the running noises are waking them up. I was very apologetic, of course, and said I will make sure it’s better.
My kids were barely allowed to run before (even before I knew they had a baby) but now definitely not at all. Sometimes they take a heavy step or walk fast, and I find myself shushing them. I’m hyper vigilant now of any noise they make - sometimes they drop a toy/book and I find myself getting anxious the neighbours will complain again, but I know I can’t do anything about those noises unless I literally do not allow my kids to play with any toys or books.
I’m in snowy Canada and we do try to leave the house when we can, but sometimes the weather just doesn’t cooperate. I’ve started doing too much screen time too just so they’ll sit still which I feel isn’t fair for them either

also it goes without saying this is all during daytime hours as they are in bed from 7:30pm - 7:30am.
I really feel for them with their baby, having been there myself twice, but I feel like sometimes even a chirping bird was enough to wake my sensitive sleeper. How much of this burden is on me vs how much of this is just a part of apartment living?
My main question is - how do I navigate being a courteous neighbour with also letting my kids live? I told the neighbours to please let me know if the noise continues to bother them but I’m not sure what I would say or how to handle it if they come back saying it’s still too noisy as I’ve done what I can. What do I say if they come back? I feel like they’re the type to pursue a formal complaint with the building management which stresses me out too. Any advice would be appreciated.