Imo Rust already has the perfect book. I would make a resource for C developers. Especially since you know C already.
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Writing a book when you don't know the subject matter doesn't sound likely to result in a good book. Even more so for a language like Rust, which (short of Haskell) is the closest thing to a mainstream language that is informed by a lot of pointy headed PL (programming language) theory. A book about programming in Rust doesn't have to go into the theory per se, but the author should be familiar with it, just like someone who writes an introductory calculus or statistics text really needs a much deeper mathematical background than the book itself will convey.
If you want a Rust-related hobby, first of all, why not do Advent of Code in Rust, or otherwise make a study of Rust? And then if you're interested in PL theory, that's another area to study. Harper's book PFPL is a good place to start: https://www.cs.cmu.edu/~rwh/pfpl/
I'd say going with C is not a bad idea at all—I for one would be interested. C is not going to become obsolete any time soon and is an immensly useful language to be proficient in.
When I tried to learn C I felt like I'm doing everything wrong because the C-way of doing things is very different to what one is used to from more modern languages (header files, make etc). Bridging the gap between the "I can solve project euler challenges" stage and actually being able to organize and implement proper projects is difficult without a mentor, so why not share your expertise?
In the end, go with what you feel most like doing, there will be an audience either way. So pick what is most fun to you!
Rust is definitely not new and niche anymore, its the most popular language in the StackOverflow surveys.
A C book feels dated at this point, there are very strong recommendations that C is to be phased out in favor of memory safe languages. But people have been signalling the death of C for decades, so it probably has a few more years left.
A good C book on how to write memory safe C would be useful. Its been tried many times, but newcomers to C still seem to struggle with allocation and freeing, and thread safety.
Do both but only publish the C tutorial. Only do a Rust translation as a draft so you can learn Rust. It would be wildly irresponsible to publish the Rust translation when its the first time you've written Rust.
C
I don't see how that is relevant? You're already familiar with C, so writing about C does not influence whether you will be outdated in a few years. Learning and writing about Rust could be something that becomes useful, but not necessarily practically - it depends on what you will do in the future.
If you feel you lost your passion, I would suggest learning and experimenting with Rust. It's different, so may be interesting and thought provoking to learn.
Writing down what you know about C may also be worthwhile, good, or produce a good resource, but I don't see it as much or like as sparking lost interest and passion. If that is actually your goal (you only asked about future relevancy in the end).
Zig could use your help I think. Give it a look
I'do go with c. Sent a link to us when you start!