When I search, I get the option to pick which instance to run the search on.

However, the search runs across all content that that instance knows about, so content from other servers is shown in the results.

When you use the search in Liftoff, it takes you to pick an instance that you’re searching from. It should hypothetically be a search through all the posts that insurance knows about, meaning everything on the insurance and all instances it is federated with.

In-browser, I know that Lemmy.world allows you to search among your instance’s communities or among all (known, federated) communities. It would be nice if that were an in-app option.

This confused me too, but it’s choosing which account you’re using, not where you’re searching. Your search is still across instances.