Another Dr. Stone fan here. I will definitely vouch for this show. You have to go in being prepared to the anime-ness of it all - this is not actual science and engineering any more than your average "spokon" show represents the actual practice of whatever sport it involves. It's not accidental that Riichiro Inagaki, the writer of the manga this show adapt, previously worked on Eyeshield 21, a hilarious and over-the-top take on American football, wherein Japanese high school teams field running backs as fast as anyone in the NFL and there's a guy who is 2.04 m tall, weighs 130 kg, and regularly breaks his opponents' arms by tackling them as a tactic. He's also currently writing Trillion Game, a series that takes a similar bombastic approach to the world of start-up founding and venture capital.

The essence of this approach IMO is to represent not the actual thing, but a sort of abstracted and stylised spirit of the thing - all emotions dialled up to eleven and compressed. But at that, I think Dr. Stone really excels. It may be one of the most genuinely humanistic works of science fiction ever made. It is still far more willing to delve into the science and technology of the various devices that get McGuyver'd to fix the problem at hand than any other fictional story featuring some kind of genius protagonist I've ever seen, and at the same time it has deep love and respect for all aspects of human craftmanship and ingenuity. It is very adamant that for all his genius, protagonist Senku couldn't do much without his cohort of friends who put in a lot of hard work and combine their various skills, which include both manual abilities, brute strength, and soft skills such as psychology and business sense. And it really drives at the emotional core of science, something that we don't see often. Most fiction and popular culture puts science and emotion at odds. Dr. Stone shouts in your face that science is beautiful, AND cool, AND one of the best human achievements ever, both in itself and because it makes people's lives better and happier. There's a scene where a short-sighted character gets her first pair of glasses and if you can relate to that? It will make you cry.

A side note as a manga reader for this: the story is over, and I think the new season of the anime that's starting next year will wrap things up. As it often happens with long running stories, the quality isn't constant all throughout - there are some arcs in the middle that are somewhat less compelling than the absolutely banger beginning. But for a manga it has what I would consider a very good conclusion, which still makes it one of the most satisfying reads around in a medium that is infamous for its tendency to fizzle out with bad poorly planned endings. Another thing of note is that Boichi, the artist, is famously a classic sci-fi aficionado, and I'm sure his influence is all over this work too. Without going into spoilers, the ending and explanation for the petrification necessarily veer into high concept sci-fi, but I think it's quite the interesting take and it should probably also find a receptive audience between the readers of this site. So, you know. Go read/watch it.

I'm glad this helped you, and think it's cool you wrote up this recommendation, and I wish people did more of that sort of thing.

I felt very disappointed by this show. It fell into a lot of anime tropes I find cringey and misleading, but worse, I felt like the characters acted very irrationally and uncarefully, and in my opinion aren't good role models of rationality. 

E.g to pick a few early not-very-spoilery points, they don't optimize their first deliberate de-stoning, and even though it's known that when stone people break they die, they choose to carry a stone person they value highly, including running with them through the forest (which seems like it could easily have resulted in tripping and breaking them) instead of un-stoning in situ. Senku contends that Taiju shouldn't let himself die to save Senku because both their skillsets are needed, but Taiju's is about being physically strong (vs Senku being exceptionally smart and good at science) which is clearly a more common skillset (and easier to identify in petrified people). 

Also, Senku contends that counting is "simply the rational thing to do" but that doesn't seem obvious at all; for most people, that seems pretty unlikely to be the right approach to maintaining sanity. 

Nice to see more fans!)) I have also written a review with more focus on rationality demonstration within the anime: https://www.lesswrong.com/posts/yqXoFx7jsSjbWgvBq/review-dr-stone.