A lot of anime set in the distant future doesn't specify the calendar year, so it ends up with something like "Before the..." or "XX years ago".
Some of the future-themed anime such as Gundam and Dragon Ball have their own calendar era which is Universal Century and Age respectively. We can't convert or compare the alternate calendar of the Anime to our real-life Gregorian calendar, so it might be helpful if the Anime has a similar calendar to ours.
According to my research, Legend of the Galactic Heroes is the anime that is set in the most distant future as of today, in AD 2801.
Looks like Legend of the Galactic Heroes is the Anime that is set in the most distant future (AD 3596). You can squeeze it in or append the list if you found any Anime that is set in the era between the Anime(s) or further.
Yuji wakes up from cryogenic sleep in 2031 and the story begins.
Ergo Proxy: Year set in 7207,It is the only anime that is set in the most far-distant future (Excluding the other Animes). The story takes place in the year 7207 where earth takes more than a thousand years to recover from a Global environmental disaster
Land of the lustrous: (Unspecified) The anime is set in a Far, Distant future where the earth is struck by meteorite 6 times, ravaging it in the process.
Legend of the Galactic Heroes: Set in 3596
Girls last tour: some post-apocalyptic dystopian anime, No doubt the anime year is likely set in 3230 (As given by the camera of Kanazawa), where Yuri and Chito continues their journey at the near ending of the world
Nausicaä of the Valley of the Wind: c.3118
Harlock Space Pirate: AD 2977
Cyber city oedo 808: Set in Year AD 2808 at Futuristic Tokyo, Japan
Halo Legends: The story is set in year 2775 Which follows Different timelines in the galaxy
GUNNM: 29th century. This anime has a lot of timelines in the future
Dirty pair flash: Year 2248
Megazone 23: The story takes place in More than 500 years in the future
BlazBlue: Alter Memory: Set in the year December 2199
Dirty Pair Project Eden: Set in year A.D 2141
Ultraviolet Code:044: Set in 2140
Darling in the Franxx: the battle began in the year 2037 and currently set in the year 2137
Appleseed: The story begins in year 2125
Dirty pair OVA: Year 2118
The Animatrix: Set in year 2090
Iroduku: The World in Colors: It takes place in the year 2078 in which time-travel is possible.
Planetes: Year 2075
Cowboy Bebop: Year 2071
Vexille: Year 2060 to 2067
Macross The Musicalture: Year 2062
Macross frontier movie: The wings of goodbye: Year 2059
Macross The ride: Year 2058
Mardock scramble: Set in the year 2054 in the futuristic city called "Mardock"
Genesis Climber Mospeada: Set in year 2050
Macross Dynamite: Year 2047
Armitage III: Year 2046 takes place on a futuristic dystopian society of mars
Ghost in the shell Sac_2045: Year 2045
Bubble gum crisis Tokyo 2040: year 2040
Arpeggio of blue steel: Year set in 2039
Dr.Stone: Near future in year 2038
Dimension W: In the year 2036, a fourth-dimensional axis called Dimension W is proven to exist.
A.I.C.O. Incarnation: Set In The Near Future In Japan --> Year 2035