I was reading the Wikipedia page for the Epic of Gilgamesh, and this line caught my eye: "Although several revised versions based on new discoveries have been published, the epic remains incomplete." The source for this line is from 2003, so I googled the topic and apparently 20 new lines were discovered and announced around 2014-2015. So my question was, as of 2021, what is the current status of the Epic? Is it considered complete? If it is incomplete, do we have some idea of how much we're currently missing?
No, it is not complete, but we have a good idea of how long it originally was, at least in the Standard Babylonian version (the 'classical' narrative from the 1st millennium BCE, not its predecessors).
The reason we know this is that the epic is divided into twelve tablets, or chapters, each with about 200-300 lines of text. These are physical cuneiform tablets (the amount of text that fits onto a clay tablet), but also narrative units. For all of these tablets, several copies are transmitted, and the copyists often very kindly tell us in a so-called colophon at the end what the number of the tablet they are copying is.
There are about 75 manuscripts of the epic in existence, however, none of them preserves the entire narrative. This is because all copies of the Gilgamesh Epic that exist are ancient texts on clay tablets, found in archaeological excavations, and more often than not, these texts are quite broken and only preserve some lines. We only have the more or less complete text for five of the twelve tablets, the rest is quite fragmentary.
This is partly due to the accident of archaeological discovery and partly due to the fact that already in antiquity, there seem to have been more and less popular parts of the epic, so some tablets/chapters seem to have been copied more frequently than others.
Luckily, in some instances, the storyline can be reconstructed based on earlier and parallel Gilgamesh stories, but, overall, George estimated in 2000 in the introduction to the Penguin edition of Gilgamesh that about 575 lines are still completely missing. This number has decreased since 2000 with the discovery of new fragments and it will likely decrease further in the future, but chances that eventually all the missing lines will be discovered are rather slim (the 20 new lines that were identified in 2005 were a very unique and exciting discovery and not something that happens every couple of years).
For a good initial overview of the Gilgamesh epic and its transmission history, I'd recommend the introduction in A. George (2000): The Epic of Gilgamesh. A New Translation. Penguin Classics.
The most recent critical edition of the entire epic is by the same author: A. George (2003): The Babylonian Gilgamesh Epic. Oxford University Press.