How can I do this?" text animation

You are going to need each line on a separate layer. I tried to use a Path on a text layer to create the curve and I can't come up with a combination of text animators that will space out the layers. 

I don't have time to generate the expression now, but if you create a null, parent the text layers to the null one at a time as you rotate the null to evenly space them out, then create an if/else expression that looks at the toComp(anchorPoint) Y value to generate the t in t(t, tMin, tMax, value1, value2) expression you can use the text layer height plus some padding to move the layer out on X by animating the anchor point.

If I get time later, I'll fiddle with the expression to make sure that it works properly. 

I think you should be able to use a text animator for the displacement, something like this set up:

Alternatively, if you're wanting more automation, then I'd try having each text on a separate layer and use a collision detection to determine when they need to pop out.  Dan Ebberts has an example expression and tutorial on this: https://www.motionscript.com/design-guide/collision.html#:~:text=The%20basic%20idea%20is%20that,that%20a%20collision%20has%20occurred.