I wonder, how to integrate a story (storyline of some sort) into 4X? I find it especially difficult to tie the story with the 4X mechanics (how the narrative connects/interacts with the rest of the game which is a strategy).

For example in Endless Space 2 you have this predefined main storyline (one per race) where you are presented with a series of chapters (disconnected, linear, presented one by one) where you always have 3 options (3 tasks to choose from tied with a reward) and to proceed the stoy you need to finish one of those tasks (4X style: spend X of resource Y, collect X of something, go to location X, etc). Which is kind of, well, not good at all

This is an open question, feel free to interpret it any way you wish, I just wanted to research this topic

Typically, a story is about people and a 4X game is about empires. This gap is very hard to cross without serious compromises, such as the impersonal and rudimentary "stories" of races in the OP or focusing a 4X game on characters in order to have something happen to them.

A game series that has done something similar is A Valley Without Wind.  In that series, you have a character that's running around, rallying the troops and such, and the plot progresses when the rebellion building hits certain milestones.