If the Terrarian's height is taken to be the same as Steve's, then we can tell by placing Gold Bars that 4 Gold Bars=1 Block in Terraria, and if 3 blocks are needed to reach The Terrarian's height, then 1 Gold Bar in Terraria would be equal to 1/6th of a cubic meter of gold. The item that takes the most gold to craft is the throne, taking 30 of these bars each (they can also take Platinum but the looks don't change so it is to be assumed that the Terrarian can transmutate matter). Each of these thrones weigh about 96600 KG each. The Terrarian has 51 inventory slots, including the trash slot that can act as an inventory slot. Thrones can stack up to 9999. As a result, The Terrarian can carry roughly 49261073400 (About 49 billion) kg worth of gold. For reference, assuming that the old recipe for the Enchanted Golden Apples are still canon (involving 8 gold blocks per apple), and that Shulker Boxes (27 slots) are not interdimensional storages, taking into account that Steve can carry 37 Shulker Boxes and that the stack size in Minecraft is 64, Steve can carry 9871718400 (Almost 10 billion) KG worth of gold. It is to be noted that The Terrarian is actually slightly shorter than Steve, which I didn't know until recently, which would make this calculation slightly inaccurate. However, The Terrarian would still be far stronger.
As a disclaimer, I am not trying to say Terraria is better than Minecraft or anything, or trying to get people to insult either game. Both games are great for different purposes. I just did this because it was stupid and funny.