Thanks for your help. I have tried it already with the sourceRectAtTime() but it hasn't given me the center of the text layer, because the anchor point doesn't unfortunately start in any of the corners. And with any change to the text the offset values change as well.

Is there a way to get the center of the red bounding box? Or is there a way to fetch those additionally needed offset data to use in an expression?
Christian
To clarify, are you using paragraph text, or point text? (drag a box vs click)
While many things work the same, paragraph text can come with a few extra complications.
You've got a variety of functions available to you using sourceRectAtTime, which should allow you to get what you need.
For example, adding this expression to the text layer's Anchor Point will keep it centered on the bounding box, observing multiple lines, line spacing, ascenders/decenders, strokes, etc.
var rect = thisLayer.sourceRectAtTime();
var x = rect.left+rect.width/2;
var y = rect.top+rect.height/2;
[x,y]