There is no fix that doesn’t add a layer from above or below. Carpet tiles seem easiest. Maybe a sound machine on timers in their bedrooms.

I'd put down a couple area rugs and call it good. With only one layer of wood like that between the spaces the kids are going to have to acclimate to sound in any event (which they will, after a while). Another layer of added flooring won't do much to block that.

Nice floors-- isn't it interesting how old utility/subfloors have so much more character than the new flooring we install now.