Ah, this is my time to shine! I used to be a part of a horror and sci fi theatre company, so this is my forte :]
There are two books that contain sci fi plays: Six Science Fiction Plays by Richard Elwood and Geek Theater by Erin Underwood and Jen Gunnels. The first I managed to find a cheap copy of but is mostly screenplays, the second I've been told is wonderful and contains a play I actually did see which was August Schulenburg's RUR--which was a meta re-imagining of the original RUR by Karel Capek (which is the play thought to have brought the word "robot" into the English language). I enjoyed Gus' RUR quite a bit. I am slowly getting through Elwood's Six Science Fiction Plays, but it seems to be mostly screenplays and teleplays, so the title is pretty misleading.
As some have mentioned, Via Galactica is both a mess and a reason why sci fi hasn't translated well into MT (some of the songs really are fun though). I do think that in the hands of the right people, it could've been more successful--but as most have echoed, it's hard for straight sci fi to translate into musical theatre without it being camp or parody. I think part of the reason for this too is that audiences are conditioned to think that sci fi is something for the movies, not for the live stage which leads to bias going into a lot of these kinds of shows--and in fairness, sci fi can be brought to live in Hollywood in much more believable ways with special effects budgets. But even still, tone is a consistent problem in the genre, especially in musical theatre.
Also to echo some sentiments, I think Broadway is a tricky place for genre work (fantasy is great, but sci fi and horror it's way harder) and I do think a large part of that is the size of the house. I think sci fi and horror on stage usually works better when it's a more intimate experience--the more it's blown up, the harder it becomes to really control the tone of the experience, and almost always leads to undesirable production choices.
I'm also of the belief that in live theatre, stories built around dystopias tend to do better because they tend to feel more "human" and grounded in the "familiar"--I thought 1984 was a stunning example of this back in 2018.
However, I think culturally at this moment, our appetite for dystopian theatre is slim to none, seeing as we're living in one--but depending on the piece and the creative team, could also feel quite cathartic. To this end, I know there have been operas/stage adaptations of The Handmaids Tale, Fahrenheit 451, and Brave New World--they just haven't reached Broadway (although they've been done regionally). That being said, I will also say it's a genre that tends to lend itself better to straight plays as opposed to musicals, as well. A Clockwork Orange has been done to degrees of success (although the version that exists operates more as a play with music IIRC), although the most recent revival was simply dreadful--they attempted to tell the story more abstractly through dance with perfectly, traditionally attractive twinks and it was a complete waste of time. (I should also think given our current cultural climate that our appetite for any future revivals of ACO especially given its graphic content, are probably at an all-time low).
Here are some other links worth checking out: Wikipedia's science fiction play section , science fiction musicals section, 5 Dystopian Novels Adapted for the Stage by Theatre Mania.
I'd also recommend some of the following plays:
Far Away or A Number by Caryl Churchill (most of Churchill's work is fairly dystopian), Really Old Like Forty-Five by Tamsin Oglesby, Mr. Burns by Anne Washburn (her work on the whole operates within the scope of 'geek theatre' pretty well), The Nether by Jennifer Haley, Babel by Jacqueline Goldfinger and Mac Roger's The Honeycomb Trilogy.
I'd also recommend checking out the Forum for Science Fiction in theatre.
