Space Battleship Yamato (1974)
Created by Leiji Matsumoto, Yoshinobu Nishizaki, and Eiichi Yamamoto, Space Battleship Yamato follows the crew of the titular starship on a mission to get technology that could save Earth during an interstellar war.
Admittedly, the original series is hard to find in the US at the time of writing, and I have not seen it personally. Nonetheless, Space Battleship Yamato is a well-regarded series that has been influential on Japanese sci-fi series in a similar way that Star Trek has on American and Western sci-fi.
Urusei Yatsura (1981 and 2022)
There are two anime adaptations of Rumiko Takahashi's sci-fi romantic comedy, Urusei Yatsura (which roughly translates to "Annoying Aliens"). Both are fun and follow the misadventures of a human boy, Ataru Moriboshi, and an alien oni/ogre princess, Lum. Urusei Yatsura is also referenced a few times in Star Trek: The Next Generation.
On top of having some zany elements akin to Star Trek: Lower Decks, Urusei Yatsura builds an intricate world mixed with space aliens and creatures from folklore without ever taking itself too seriously. It does not wrestle with moral quandaries, but it has the distinct feel of light-heartedTrek episodes, like "The Trouble with Tribbles."