I mean, we could speculate and explore the strange future and stuff. Just without that tired trope of "well, science and technology progressed a bunch and then we got this really great machine".
Pretty much all of the Sci-Fi written by Ursula K. LeGuin features people more than machines. There are technologies in the stories that play a role, but the are described as vaguely as possible to support the plot. As a result, often her sci-fi stories feel more like fantasy.
Octavia Butler wrote the Xenogenesis series which features an alien "species" whose system of technology is entirely biological.
I mean… steampunk pretends to emulate modern tech all with steam power. Not only is it so absurd that it’s funny and enjoyable, but aesthetically when bathed in art deco, it’s positively gorgeous.
But in terms of story…. Shrug, there are probably tons of sci-fi writers that have touched this kind of storytelling. I think Alan Dean Foster maybe had something like this, and/or Piers Anthony, maybe a few others I read many years ago. No recollection as to what actual books, sorry.
Children of Men would be a sci-fi without any significant technological improvements. Ender's Game does have the Ansible, but it's more a plot device than anything.
I read a cool short story a few years ago that really embraced that quote. It started out as a fantasy story with wizards doing magic. It then turns out that magic is actually old nano machines or something, but society has forgotten all about the science behind them.
Probably not exactly matching your meaning, but in a round about way, Dune, post Machine Crusade --
It's maybe not as evident without reading the series--which definitely isn't a negative comment! I've enjoyed (almost) every bit of the truly shocking amount of Dune I've put myself through since the very early '90s, haha.
I'm, uh, mildly obsessive as well as critical of the SF I stand by, (just for myself personally!--everyone should like whatever they like!) but Frank Herbert, entirely, still remains in my top 2 favorite authors. You may enjoy all the books as a whole, if you're looking for something less about 'the machine' itself, but how humans diverge from it and without it, but it's...a lot, lol. And...well, I won't spoil things. I just remembered it might negate my entire point. Oh, no. (ʘ‿ʘ)
Anyway! Regardless!
If you do ever get into full-ass Dune--and I'd recommend this "tip" to literally anyone--I'd definitely suggest audio books for the early works of Brian Herbert and Kevin J Anderson. They took a bit to get into their groove from informational to actually entertaining. The lore is honestly fantastic, beautifully done, but physically reading their earlier Dune stuff can be textbook without diagram tedious. Love 'em both for the work, but shiiiiiiiiite.
There's plenty of star trek episodes that are more about philosophical and societal questions than tech.
The bicentennial man by Isaac Asimov comes to mind. Which is about a robot, but in essence it's about the philosophical question what it means to be human.
There's Ubik by Philip K Dick, which is about about tech, when you get down to it, but in a very unique and un-tech like way.
Flowers for Algernon by Daniel Keys is not about tech, but the chronicles of a brain surgery patient that became extremely smart.
Hyperion by Dan Simmons is basically just "The Canterbury Tales" in space.
There's plenty more stories that are not really about tech. You could try searching for dystopia themes, like "Maze runner" or "the hunger games" or "I am legend" or "wayward pines"
Try searching for authors who describe their work as "Speculative fiction" - that's the way most of them don't admit to writing low-brow schlock like sci-fi.
Also near future sci-fi tends to be a bit lighter on the "magical machine" plot tropes. Climate fiction might be worth looking into too, most of the near future books exploring possible global warming consequences aren't all hopped up on magical technological advances.
Edit: also check out various books described as literary speculative fiction. Authors who want the intellectual cred of being a literary writer tend to land in the speculative fiction genre more often than not.
What are some examples of things you don’t like? That’s really necessary to give examples. Science fiction usually has technology in some form or another. Sometimes it’s the focus of the story (eg The Last Question or Permutation City). Sometimes it’s a tool for the story (eg The Expanse or Neuromancer_). Other times it’s set dressing like magic in fantasy (eg Dune or Book of the New Sun). Outside of hard SF and beyond Golden Age SF you run into more “tech as device or background.”
Science fiction is in it's essence the exploration of a situation when all the confounding factors have been magicked/scienced away.
Not uncommonly it explores the requirements of the technical solution, what would the machine need to do for this to work out? And/or What happens if it doesn't?
Take for example "Do androids dream of electric sheep" by Philip K Dick, it's about finding androids advanced enough not to know they're artificial and how to identify and relate to them when the only diagnostic is slow, clumsy, and suspect. It's more an exploration of what makes a person than it's around the marvels of The Machine™.
During the 1900s the vehicle for science to magick with had been machines, computers and AI. Remember that space travel, fission power, psychology, modern medicine were all new, hope inducing breakthroughs just this same period.
There's also the issue that the definition of the genre came after it becoming large enough to matter. The edges between scifi, punk/cyberpunk, speculative fiction, isekai and even to fantasy are all made after the fact, meaning modern machines go into scifi, old machines go into steam-/diesel-/etc-punk. The main difference between Science, Magick, and Eldritch horror is how detailed the mechanics of the solution are described, and speak to different people.
But on the topic of the story not being centered around a machine: try the Hyperion series by Dan Simmons.
Or go the entirely other way with Ring World by Larry Niven. There's plenty of machines-did-it in the fringes, but the central theme is to figure out what would be needed for a Ring World to exist, what would happen on it, and how would it be managed. It's an exploration of physics more than anything - more "what is the machine" than "machines-did-it".
And the Foundation series (Asimov) famously explore the premise "what if sociology works", and the other details solved by throwing machines at them.
You also have The Culture (Iain Banks) series that center on/around post-scarcity society and explore that.
If I'm understanding this correctly, you're looking for fiction that focuses on framing more of cultural and societal shifts than technological changes?
What you're looking for is difficult to find in the framing of Science Fiction because its very framing invokes technological advancement - technology is the application of science, and machinery is the result of technological innovation. Science fiction is, at its core, about how discoveries in science may change the world.
Nonetheless, you may want to look into the sub-genre referred to as "social science fiction". Although it's not going to be devoid of advanced technology, the focus will be more on the social and societal impacts thereof, than the machinery itself.
What you’re looking for is difficult to find in the framing of Science Fiction because its very framing invokes technological advancement - technology is the application of science, and machinery is the result of technological innovation.
Machinery's certainly a result of technological innovation, but not the only result. Different materials, even altogether different forms of organisms are also results of technological innovation. OP's left it rather open, so it may be that they also mean these different applications of science.
IIRC The Moon Moth by Jack Vance was not really anything to do with machines but just an exploration of an alien culture. (I only read the graphic novel version.)
I think there are many such stories having to do with alien cultures.
A Pail of Air by Fritz Leiber also comes to mind as something with not much focus on machines. I think there may have been some sort of life signal scanner at the end but I think it still fits what you're looking for.
I once read a SciFi story where people lived in a way-post-scarcity world. There must have been machines somewhere, but they did not play a role worth mentioning.
Canticle for Leibowitz is a classic piece of sci-fi that spends most of its time in future medievalism but it kind of cheats in that it's both post-apocalypse and society rebuilds its tech base by the end.
Other than that it sounds like you want future fiction without all that pesky science.