There are many instances of megastructures known to the Ecumene, including some that are occasionally called gigastructures. The largest gigastructures are so large that even when mostly hollow they outmass the stars they use as a light source (though most are more comparable to a large terrestrial planet and its orbital system). As a result, many of these are built in interstellar voids where they are less likely to jeopardize entire star systems. However, these structures are inherently rare. Aside from the rarity of civilizations capable of constructing them, they are so large that for most the only reasons to construct them are as vanity projects or to provide habitation for an utterly ridiculous amount of people.
There are several forms of what is very very occasionally called a detrastructure. Most are spheres, because spheres allow for complete collection of a star's energy (although there is almost no use for this amount of energy). The rest are often rings (occasonally spheres under construction), disks (which allows for a more natural temperature gradient), or toruses (to make the construction modular and allow for artificial gravity); though there are others. Such structures are universally either very long-lived or very short-lived- if they survive post-construction, they are likely to survive for a much longer period of time.
There have been hundreds of these structures throughout history, with many still extant. Most of those easily accessible from the Ecumene are in the Chloric Vault, but there are many others. One of these has a particularly interesting history- the civilization that created it was deathly afraid of sapient artificial intelligences, but decided to construct a nonsapient intelligence to fulfill the role of a government for them. The artificial intelligence gradually became incapable of extrapolating further technological progress, and promptly decided its people would have an exponential population boom without a corresponding boom in availability of food. The gigastructural sphere it built remains intact, but is mostly uninhabited due to its ridiculous size.
Worldships include anything that would otherwise be classified as a starship, but is near-wholly intended for the transport of billions of people. Nearly all worldships one might see normally are quite a lot smaller than worlds- technically, a ten-kilometre cube could be a very cramped worldship- but those that are larger are quite the sight to behold. Some worldships are quite natural, while many are wholly artificial- civilizations which build fusion engines into gas giants tend to label them worldships to boost tourism. Civilizations often build worldships as contingency measures for proper disasters- gamma ray bursts, supernovae, or even just the possibility that future life is hostile. Quite possibly, the most impressive worldships are those orbiting the galaxy or the local group- they must be quite large to be seen through telescopes.