The Map/Information screen shows the current objective, however is there a way to know the story chapter or overall game progression?
Most of game chapters are named after characters and loading screens will feature this character. For example, "Chapter 2 - Amelie" has this loading screen:
However, obviously you need to load/reload game to see loading screens.
As for overall game progression, here are some minor spoilers which help to establish where you are at:
Total number of chapters is
Game map have 3 regions - Eastern, Central and Western regions. Western (Edge Node City) is very small, so as soon as you are close to connecting all nodes in Central region you are entering endgame.