Let's say a spellcaster is fighting a dragon. Can they ready their action to cast a Wall of Stone with a trigger of "If the dragon uses its breath weapon I block it with Wall of Stone"? If so, how high would the wall have to be made?
No, this won't work
The method for readying an action is that you use your action to hold the spell at the ready (pre-casting it), then use your reaction to cast it when a given trigger occurs.
But here's the catch (PHB, p. 193):
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. Remember that you can take only one reaction per round.
If you have readied a spell to cast if a dragon uses its breath weapon, the only time you may unleash the spell is after the dragon has used its breath weapon and the outcome of that has been resolved (finished). Meaning you will cast Wall of Stone after the dragon uses its breath weapon, and thus after you've already saved/taken damage from it.
reactions can be taken after a trigger which you state, just use the same trigger for counterspell but reword it, which is just "when you see a creature within (range of spell you're casting) of you, starts casting a breath attack"
I don't see why you can only take your reaction after the thing already happens because almost all reactions this is false and you are actively doing something right after your trigger.
Another Example would be can you hold action to cast globe of invulnerability to save a friend from a breath attack. if you couldn't that would just be dumb and screw support classes