Programming languages are tools; I would use Go for a web server, typescript for a web site, C++ for a computer game or high performance desktop app... you have not given enough details for anyone to give you a recommendation on what languages might be good to use.
Zig doesn't offer much in terms of high level abstractions and is very manual (I'd consider it far too much pain here unless for the embedded realm) - it's a better C at best, no rival for C++'s power and software design capabilities...
Rust has serious pain points when you consider the borrow checker and want to do complex stuff asynchronously, there's a big learning curve here, also not in every realm is it crucial to have memory safety (a desktop computer game is not flight control software... which btw you could also use C++ for, and it is used here, albeit w/ care). On a one man project it's also much simpler to simply write good modern C++ code than it would be on a large scale project w/ hundreds of programmers. I've also read that Rust's build system (nice as it is) has still limitations w/ very complex build setups...
And whether it's good to use C++ in 2024 for a new project... C++ will be around for DECADES at this point, it has a swath of libraries and tooling, good compilers producing optimized output targeting everything under the sun... yep, it's not part of the "hype around town" languages on Reddit or other boards, but C++ is used every single day in almost every industry down the line by millions of programmers!
What exactly is your worry? That you can't compile your code from 2024 in 3 years? Relax about the online hype... there are areas where EOL languages are still used... C++ isn't dead yet, won't be for a long time. It won't pick up steam any time soon it seems, but for what it can do (including its tooling and libraries) it's hard to beat, and it's not obvious to me that Rust and Zig are obvious "successors".
Zig isn't even at a 1.0 version yet w/ no clear roadmap to get there... I'd be much more worried using it for a serious project than C++... and C++ knowledge will be better on your CV than "Zig knowledge" (which most people won't even have heard of).