Shipping rules during checkout

I’d like to display a text during checkout that says something like “Order stuff for another XX€ and get free shipping!”. For that I somehow need to access the shipping rules data in the template.

However, I don’t know which variable - if any - contains this information. Is there documentation on this somewhere?

Anpan, can tell you where there’s a source code documentation but scarcely know which specific getter to use (or maybe have to write your own):