Rust is relatively new language. A lot of people in my context are using Software with C++ or .NET applications or Python.
Is there any existing project that can help to embed RUST as an editor to 3rd party software that has C++ or .NET opensource backend? So that people could embed RUST into existing software packages?
Rust is not a scripting language like Python, so the answer may be no if that is the sort of embedding you're imagining.
If you want to call Rust code from C++, you write a Rust library. The Rust library will export functions that can be called from C++ using C calling conventions (this is called the C ABI). This is the FFI (foreign function interface) of Rust, and is documented here:
The short version is, unfortunately "it depends": the key word here when installing Python packages is "Wheels" - pre built versions of a package that (when they include native code such as C or Rust) are specific to a platform: for example operating system and CPU architecture.
So "most of the time no, but only if you get it right"
Rust programs don't need an external runtime to run. Compiled programs don't need Rust installed. In this regard Rust is like C or C++, and different from Python, C#, or Java.