Is there a way to share a tight staircase/steps with pedestrians?
I've had to commute routes where I need to use a narrow staircase to go up and down a pedestrian bridge over a highway.
For starters, any place where you have to share narrow space with pedestrian, the polite way to do so is to dismount.
I shoulder the bike or walk it. The bike always goes to the far side ( If there is  a fence or wall, the bike goes towards that fence or wall or guard rail. ) so there is less chance to hit another person with a protruding pedal or handlebar.
While going down stairs, I sometimes roll the bike on its rear wheel, holding the handlebar up and using the brake to control it. That way my combined bike+rider width is minimal and that will let another pedestrian pass, even if they are also carrying a bulky load.
Consider that even if you believe to have good control over the bike, there might be something out of your sight that may cause you to temporarily lose control or may need you to perform an unexpected maneuver (e.g. a piece of garbage you ride over and it makes you lose traction). If that happens at the wrong time, you may hit another staircase user. Better to play it safe and dismount.
I've ridden in a city where there are shared bridges (pedestrian/alternative transport) but it is mandatory to get off your bike, skateboard, or whatever you are riding. You mount again on the other side where there is a wider and dedicated cycle path and a walking lane.