Off the top of my head:
Scheming with lords (special quests you can do with lords you have high relation with)
Insulting and then dueling lords
Feasts
When you attempt to sneak into a town and fail, in warband you had a chance to "fight your way out" which involved fighting 5 or 6 guards while wearing your disguise robes and wielding nothing but a stick
Learning poems from bards, and reciting them to ladies to gain relation with them
Purchasing and reading books
Having a village your have high relation "cause a distraction", which reduced the number of guards you had to fight when breaking someone out of prison
Companions were premade (not randomly generated) and each of them was incompatible with 2 others, and if you had 2 incompatible companions in your party eventually they would argue and you'd have to choose to support one, and the other would eventually leave you unless you could persuade them to stay. Some companions would also get along particularly well, and would share that with you. Also with companions, when you traveled by a certain city relating to their backstory, they'd stop you and tell you some stuff about the places history. Companions would also complain about way more things. In Bannerlord you might have noticed someone complain about you raiding a village, except it doesn't mean anything. In Warband, they'd complain about that as well as running out of food, failing quests, and running away from battles. These things would make them unhappy and if they got mad enough they'd leave.
In warband when clicking menu options in settlements there was a chance you'd get waylaid by assassins, and you'd have to fight a couple bandits in the town at night by yourself.
Belligerent drunks; dudes in taverns who would randomly insult you and then attack you
You could find exiled claimants of every kingdom in towns. Instead of pledging to a current faction ruler, you could help the claimant retake their throne and become the new leader of that faction.
You could set up camp wherever, and wander around your campsite. Admittedly there was no point to this, and the main function of setting up camp was that it just brought up another menu of options like choosing to retire from adventuring or choosing a book to read.
The ability to accompany parties on the map
Oh, and you could actually buy good armor from shops.