Haven't seen Lexx. Heard it was more dirty jokes than honest-to-goodness sci-fi.
I'd like to add Mass Effect to the list. It's not a series of shows/films though, it's a game series. The trick is to get the remastered trilogy. The first one sucked, and the remastered version fixes everything wrong with it. People love the first one in spite of all its problems. The second and fourth ones are the best, though the fourth one is its own thing. All the online is gone, the remastered third one gets rid of it, but the fourth one still sells online crap that don't work.
If you're unfamiliar with the story, here's a crash course: humanity discovers an artefact on Mars that allows them to slingshot to a faraway galaxy. They send an expedition and find a friendly group, kind of like the Federation but more loosely knit. One of the main races sponsors humanity, takes them under their wing, and some species think humanity got elevated too quickly. You play the first human SPECTRE, which is kind of an interstellar free agent who investigates things and carries out the will of the council (which is mostly worthless as we soon learn). Another SPECTRE murders one of your guys, and the council doesn't believe you, but they rush your promotion so you can investigate independently. Turns out it's more than that, he's trying to resurrect an ancient race that wants to destroy everything.
The game was made after developer BioWare lost the Star Wars license, so there's a bit of Star Wars in Mass Effect in that you can get psionic powers. They're optional, you can roll a soldier class, but they can still be used against you, and some of them are pretty cool. But it's also like Star Trek in that you can explore solar systems and land on planets and explore. It really is its own thing, and if you buy the remastered trilogy, you have something like 150 hours of gaming, and it goes on sale for less than ten bucks (I got it for $6) all the time. I paid $4 for a deluxe edition of the fourth one that came with some online crap I can't use. I'm not even mad. Woulda been $3 without it. I think I got 20-30 hours out of that game.
Starfield is probably the most Star Trek-like game out there, but Starfield sucks. I say this as a Starfield player. Paid $30 for it on sale last month, but I previously played it on GamePass, and I have over 800 hours in it. It's not a great game by any stretch and I'm kinda mad that it's worse than Mass Effect in almost every way, despite being about two decades newer. That said... you can build a ship from parts, then walk around it, then board it and walk around in it (they can be quite big!), then take off, then while in space, get up again and walk around, take the stick, and dogfight in it. The game itself sucks for a lot of reasons, but there's something to be said for building and operating and upgrading your own ship. And Constellation is like a shitty Starfleet, with the morals and all that... You can do some dastardly deeds, but all your allies will turn against you in a heartbeat for some things (not all). Still, if you want TOS, do the Vanguard and Ranger quest lines, if you want TNG, do the main quest, and if you like DS9 (and Section 31), do the Ryujin quest. Or the pirate quest and side with the Vanguard — you'll still get the best gun in the game. But I like the pirates
Then of course there's Cyberpunk 2077, but that's more "sci-fi/body horror" and "Cyberpunk" and not really Trekker stuff. But, it does feature Keanu Reeves, Idris Elba, and Cherami Leigh. So there's that.
You can sit and watch... or you can be part of the story. I think that's the future. Sadly there hasn't really been a good Star Trek (or Star Wars, for that matter) game... but Mass Effect is a great game made for Trekkers. Starfield is a kinda-bad game also made for Trekkers. But it's better than most Star Trek games.