I'm making a mountain dwarf, battlesmith artificer that has proficiency with most Artisan's tools. Using the proficiency swapping in TCoE, I got 4 more tool proficiencies from Dwarf and are only missing 6. Mountain Dwarves have proficiency with light and medium armor, and I'm wondering if that gets me 2 (Because I trade in all light armors for 1 and all medium armors for 1) or 8 (Because each different armor such as leather, studded leather and half plate, all get me 1 each) proficiencies.

Light Armor is one proficiency and Medium is the other. So replacing Dwarven Armor Training gives you 2 proficiencies - and that's how DNDBeyond does it.

As far as I'm aware there's not a single instance of being proficient in an individual type of light armour such as Studded Leather and not being proficient in all the rest. The same goes for medium and heavy. It's all of a type or nothing.

Ok, thank you.