The UK built a crayfish processing facility so that they could have income. They also sell stamps and a few handmade crafts such as knitted socks. There are a few government jobs and they must make some money from tourism. And they all grow potatoes for their own consumption.
There's actually Street View images, so you can take a look, also at the agricultural plots southwest of the town (see https://en.wikipedia.org/wiki/Potato_Patches ). There's some sheep, cattle and (I think) donkeys as well.
Lobsters. https://www.bbc.com/future/article/20250915-tristan-da-cunha...