I would use a self closing hinge for sure.

Go to a baby store, they will have options that are reasonably priced, and go high enough up that the older ones won’t be able to either reach or operate. Up to you to actually use them though.

Any specific recommended self closing hinge? (I know little of this topic). Do some closer "easier" or softer than others?

Years ago with 4 little ones we just put on a hook and eye up high.

You don't want to restrict access by the older one, just the younger one, right? I would worry about a gate if it would be opened by a 4 year old, too easy to tumble down the stairs and you still would have the problem of him not closing it. It seems the self closing hinges are not as likely to smash fingers as a hydraulic closer would. Hope someone can recommend a brand/style for you.

They are adjustable. You may need to play with it a bit. Use one of these hinges or similar or even easier may be a hinge pin door closer like this. Not as strong but still decent.