I found this out when pondering the game and the Elder Scrolls lore. In the book series, "The Real Barenziah", she is born around the time when the first Septim came into power. She was ~500 years old during the happenings of the first Elder Scrolls, the first four Elder Scrolls game take place at roughly same time and Skyrim takes place about 200 years later and ESO 1,000 years before that. That is exactly the problem! If she is 500 years old during the Arena and Skyrim take place 200 years after that and ESO 1,000 years before then that means one of two unlikely events must have happened:
A: The war that is taking place during the events of ESO is a different war then the one from whence the septim dynasty arose.
B: The war that is taking place lasts for 300 years, and that's at the point where you're starting in and who knows how long said war has already been going on before you get into the picture.

Barenziah is born in 2E 893. The alliance war this game takes place in begins in 2E 582. The Interregnum in general starts around 2E 430 and lasts until around 2E 852(?). No plot holes, just multiple wars were started during the 400 year Interregnum, one of which is the alliance war we will participate in.