[2021] A question for the math scholars

However, if you use a defensive catalyst on your jewelry, the mod becomes 24% chance to guard with 240% more armor

No it doesn't. The 200% is not a stat value.

This mod is mechanically exactly the same as when it was described as "with double Armour", the description was just updated for consistency because there's now another way to set the % of your actual Armour value you defend with to a different value than 200%.

Also, the stat gives a chance to defend with 200% of Armour, not 200% more Armour.

Also, how does this interact with having other forms of 'defend with armor' like if they have a different amount? (For instance, defend with 120% armor while not on low ES)

If you try to defend against a given hit with multiple different armour values, the highest will take precedence.