If the ideas cross with that of Space Pirate Harlock and Galaxy Express 999, Earth does both okay and not so okay. There are human colonies all over the cosmos in those timelines it seems, but Earth itself is kind of the forgotten backwater that thinks too highly of itself. Most of the population has seemingly moved on to other worlds scattered all over at least two galaxies. Humanity has some rampant problems with Machine Men and the occasional inter-dimensional aliens races. Earth sometimes has issues with more normal alien invasions, that it is either ill equipped to repel, or fights long wars, but losses for a time until the enemy can be repulsed later by Humanities seemingly rampant pirate/rebel forces.
All depending on which Matsumoto film/series you happen to be watching, since the timeline for those is a complete disaster that doesn't make sense unless you use multi-dimensional and/or history repeats itself when it comes to the heroes being multi-generational reincarnations of sorts.
Sometimes Earth still had wave motion guns, and always have wave motion engines. Sometimes the they have fleets that could handle the types of threats we normally see in Space Battleship Yamato, and sometimes their space forces are a joke that are a pushover for everyone its seems, aside from maybe a small handful of reasonably powerful battleships. In others, humanity is fine, but the space defense forces use combat space trains instead of warships for most instances (usually fairly effective). In all, there are a small number of extremely powerful, basically indestructible pirate battleships that can take on basically anything in the universe, if given enough time to figure out what the problem is, and sometimes there is also some potentially extremely overpowered Earth space battleship, that has serious technology issues (the ship's wave motion guns are way over powered, but everything else is kind of terrible, and the engines are poorly designed) ~ Cosmo Warrior Zero. With there possibly being a rebuilt Space Battleship Yamato out there someplace, that can take on anyone that gets past Harlock's groups.