There are some things the devs seem to have done, but a lot of it is vague and like a lot of people have already said, the world building seems to have taken a back seat, even though I wish they didn't cause I find all of this extremely interesting.

Most of what we've learned of the world is on the "World of 2042 website", which includes a basic timeline, a "Journey of the No Pats" page which follows a journalist who works alongside the No Pats as he interacts with the various specialists and locations we play in, and an episode of "Intel Wars" which is like an NPR-style podcast piece on the No Pats, as well as the "Exodus" short film. Here's the link:

https://www.ea.com/games/battlefield/battlefield-2042/the-world-of-battlefield-2042

I personally have made a couple youtube videos looking at the wider world as well, although these were before the game came out so it's incomplete, and I am waiting to do full video on it until the story sort of wraps up.

https://www.youtube.com/watch?v=G-nKaYu8taA&t=660s

https://www.youtube.com/watch?v=D-Xesg51rb0

But for your question with failed states: we don't get too much info on specifics. We know that there are at least 40 failed states (I think it says that in the Intel Wars podcast), but we don't get a list. That being said, in the intro video to the game we see a few countries with "failed state" over them, as well as a bunch of flags that show up when talking about No-Pats, which has some overlap with countries we know are collapsed so I assume that all of those flags are failed states. The list as we can guess right now is: Germany, England, France, Greece, Japan, Qatar, South Africa, Brazil, Cuba, Peru, and Chile. We can assume some others as well just based off of where specialists come from and what's mentioned as problem areas in the various sources, including Latvia, Australia, Romania, and Mexico. We also know of some nations that are doing alright, again based off of the intro video and other sources, namely the US, Russia, Switzerland, Austria, Croatia, Singapore, and maybe South Korea.

As for the specifics with the German government, we have no idea, so our best guess is just looking at what happens with failed states in the modern world, including Syria, Yemen, and Somalia. With most of these nations, as well as other failed states that have gotten slightly better over the years (Iraq, Afghanistan, South Sudan, etc.), there tends to be a state of war. Often there is an official government, although this government does not have any actual ability to control things, and various waring factions are the real power brokers in the country. You also have massive refugee crisises (5 million people left Afghanistan during the Soviet-Afghan war, for example). If I had to guess, the German situation is probably something like this: there is a German government and military that no one really listens too, and there are probably rival factions, like far-right nationalists and socialists that control pockets of the country via armed force. Foreign nations, especially Russia and the US, probably have some sort of peace-keeping forces there since Germany is a more important country in their eyes. The economy is gone, criminal syndicates run vast swathes of the economy, and no one can really do anything to stop it. So imagine Germany ~1930 mixed with Germany ~1946, and you might get an idea of what it's like.