Now that I think about it: I never cared much for Tenchi OVA's world building nor background lore. I had some interest as a kid, but I gravitated more towards Tecnhi Universe's galaxy. Even though Universe had less of it, but got somewhat creative with it, despite being more straightforward. I honestly prefer Pioneer Comics Tenchi Universe, because we get to know a bit more about the galaxy, even though it's technically an alternate continuity. Sucks it went out of print, but the story at least has a satisfying conclusion, and can be taken as an extra adventure that happened somewhere in the Universe timeline before the movies.
Back on the point to the OVAs: I care more about the original cast/core group (Tenchi, Ryoko, Ryokoki, Ayeka, Sasami, Mishoshi, and Washu) than any of the Jurians, the extended family, nor do I care about the three goddesses (which Washu is one of them). The third OVA pretty much killed all of that. I appreciate somewhat the original author trying to make a shared universe, but a lot of it is shit that is all in the manual or never left Japan. With most people not learning until a decade or decades later about the extended universe. Not helping matters are that even in these spin-offs or one offs, all the characters features in those specific media are either annoying cliches, boring, or come off as lame, shallow, clones. Hell, one of the spin-offs is a 2 episode soft-core hentai that somehow made it into the States with a dub. The dub is awful; don't bother asking the name, because I already forgot. You wouldn't know it took place in the Tenchi OVA continuity, unless you looked up on a wiki page. Though there is one character that's basically a dark-skinned purple haired version of Ryoko (they don't have the same hair style though nor body type), and she's a similar backstory. The only difference being she can turn into were beast creature involuntarily, and is not a homunculi.
Outlaw Star has much more going for the world building and lore within its 26 episode run, than the decades spanning Tenchi OVA series. OS helps it case, because it remembers to have variety of humans, humanoid, and alien species spanning across the galaxy. With different factions that mentioned or hinted at, but don't take over the whole show. Yet let's you know, that things are happening or going on while the Outlaw crew are dealing with their own story and adventure.