Well, I feel here there are 2 ways of immersion, the one the player creates in their heads and the one that the in game world shows to the player. The first one, invented by the player, is too dependent on imagination and the will to go outside of what you're playing, for ex: you've just finished fighting a war and return to your faction's main town, here the player says "and we were received as heroes" or "the queen/princess gave me a trophy for my efforts", etc, as you see none of this happens in the game, but the player imagines it so he can immerse himself in the world, or give their story more dynamism.
The second one created by the game is every event created by the world itself and will guide the player through so he can create his stories, and it's based on reaction of both what the AI and what the player chooses to do (the AI chooses to start a war on the players' kingdom, the player reacts by forming an army and marchs towards enemy lines/ the player destroys a caravan of another faction, that faction reacts by declaring war on them).
Now the problem here is that, even if the player can imagine all they can, at some point the game feels short of stories because basically everything that happens is always the same, go to war, get a castle, war stops, the player does nothing, and this cycle repeats, but with deaths, rebellions and more of these situations the game will start feeling more dynamic and give birth to new situations the player can exploit, but the game needs to provide even more immersion based on reaction of the events. For example, many things are underwhelming, marriage feels too easy or its just a very simple mechanic that gives the feeling of it being an unimportant moment, deaths suffer the same thing too, you die and it feels so "ok you're a corpse now choose a heir", and you know the lack of reaction to these situations make it feel barren too, I haven't played for a while so correct me if I'm wrong, but for ex: Lords react to a marriage, but do they react to deaths? Do villagers and commoners react to the death of their king? Do they praise their new king and support him? You know, I feel like the game needs a lot of work in dialogs to immerse too. In the end, it's a roleplaying game, and the role you do needs to feel like it has a weight on the world (because mostly it does)