How do I auto displace position of objects based on text box width?

The easiest way is to use my (paid) extension Pins & Boxes.

Just create pins for the corners of the text and parent the layers to the pins. The pins will stay at the corners of the text when the text changes and all layers parented to them will follow.

Note that you only need Pins & Boxes to create the rig. The mogrt you create will of course also work on machines where Pins & Boxes is not installed.

In the simplest form it could be something like this:

mText=thisComp.layer("Text");
mPos=mText.transform.position[0];
mWid=mText.sourceRectAtTime().width;
mPad=20 //padding/ spacing

X=mPos+mWid+mPad;
Y=value[1];

[X,Y]

This example assumes left aligned text and the code would be applied to the block after the text. The same methodology applies to any other scenario, but of course you may need to account for different text alignment options, anchor points and positioning of your text.

Mylenium

There's literally hundreds tutorials and templates out there for this. Just do a search for sourceRectAtTime() or phrases like "background box adapting to text". Here's even a free script/ pseudo effect:

https://aescripts.com/textborder/

All that would be required would be to invert the logic and plug in or add the values of those bounding boxes to the other layers' positions, which would be no more difficult than linking a slider.

Mylenium