The evidence seems to suggest the opposite. Other than a lot of talk on programming fashion publications that are always more aspirational than representative (such as this site) Rust seems to have reached 0.3% of the market [1], up from 0.1% a couple of years ago [2], and while that is ok growth, programming languages with few exception tend to reach, approach, or at least point toward their all-time peak market penetration around age 10, and Rust is already 7. Any language could, of course, be an exception to historical trends, but there's nothing to suggest that is the case.
More anecdotal adoption stories are just as bleak. Even at this relatively advanced age, many companies dabble in Rust — as they did in, say, Haskell — but not many established companies have yet to really bet big on it.
The only positive is that among the low-level languages discussed on aspirational sites, Rust is, indeed, the most talked-about language, but history also suggests that that is a very bad predictor of long-term market success.
[1]: https://www.devjobsscanner.com/blog/top-8-most-demanded-lang...
[2]: https://www.hiringlab.org/2019/11/19/todays-top-tech-skills/