Mitron is referred to with female pronouns in French and Japanese, and it was confirmed that it was not a localization mistake and very intentional.
In 5.3, they pretty much say that "ours is the seat of Azem". Don't need a gender for this.
At the end of 5.0 when we rejoin with Ardbert, Emet sees Azem, which implies it as well.
If the gender was not relevant for the plot, they could just have kept it "gender neutral" and it would be just as obvious (call them Azem, call them the traveller, call them the 14th, call them 'our friend' etc. all of those namings would be gender neutral and would work just as well).
I think the fact that they went one step ahead to give Azem a gender means its important.

As I said, there are just multiple elements adding up to each other over time to lead me to the expectation that the connection with Azem is more than just "we are one of their shards".