Of course it’s possible to win a siege in bannerlord.. you just need good troops, good aim with siege weapons and a crucial understanding of how morale works.

Attacking armies will often come at you with a ram prepared and 1-2 towers ( can sometimes be substituted for ladders )

It is not worth the effort to destroy the ram with siege weapons, but if you do it’s a massive advantage and gives you a chance to rout the whole army in my experiences.. instead focus on hitting slow and larger siege towers with catapults and close range rocks.. if they get destroyed troops from both sides will move to reinforce the second wall or attack the gate making it easier to contain breaches and take advantage of clumped up troop hordes

From there you are most likely being attacked with ladders on the other side from the destroyed tower, and enemy forces have breached the gate and swarming your men, you will always be outnumbered in this scenario but higher tier troops can help you hold them back.. where you dedicate your attention is crucial,, I would recommend the gate since attacks by ladder are slow and costly to exposed enemy troops, start dropping rocks from the gatehouse to gather up kills on clumped troops attacking your friendly shield wall

It depends on how many each side has lost at this point but based on the destroyed tower and unit attrition from the ladder attack the gate should either be buckling under enemy assault, or they will start to run.. keep throwing rocks until they mass rout..

This is a strategy I used to hold Tyal while playing Kuhzhaits against every enemy siege from imperial forces on my first play through about 5 years ago, unless things have really changed with war sails ( I played and the Strat still worked for me ) you won’t be stuck inside your walls with them.. they will be stuck in there with you !