For me. I vaguely try.
I use the Empress to refer to the person.
And also in generic use of “We need an Empress” (before we got one)
“The Throne” is used when refering to the title and it’s powers in a formal context.
“The Throne has the power to”
I use “Empreror” as the gendered masculine version… if it is specifically used by the individual on the Throne.
So default to “Empress” because the first one was an Empress.
“The Throne” if refering to the position/title and the powers they exercise.
And “Empreror” if the individual on the throne chooses to use it instead of “Empress”
Of course, I might slip back to masculine-led language when I’m not looking.