For lemmy.world, they are using their previous setup used for mastodon.world: https://opencollective.com/mastodonworld

As for how you can be sure, it is hard to tell, it really depends on each instance. Even in the case of lemmy.world, while you have some details on the expenses and revenues, it's not at the level of a company audit. But that was enough for me to donate. At some point there will always be a trust element.