Spectre as a general vulnerability class is NOT fixed. And you can write perfectly vulnerable-to-Spectre code in Rust, or anything you like. As long as there are "virtual" privilege separations under the same hardware privilege level, which is extremely common nowadays (hey, it's called sandbox). It would be vulnerable on ANY processor with speculative execution, including past, current and future Intel, AMD processors, M1, M2 and you name it. No need for JavaScript in browsers. Please just read the page, it's not browser specific.
In this case the only thing one can fix is, surprise, the vulnerable code!
I heard from Zen3 silicon, spectre and friends are fixed.