Is this an official Rust project?

Yes. rustup is an official Rust project. It is the recommended way to install Rust at https://www.rust-lang.org.

How is this related to multirust?

rustup is the successor to multirust. rustup began as multirust-rs, a rewrite of multirust from shell script to Rust, by Diggory Blake, and is now maintained by The Rust Project.

Can rustup download the Rust source code?

The source for Rust's standard library can be obtained by running rustup component add rust-src. It will be downloaded to the <toolchain root>/lib/rustlib/src/rust directory of the current toolchain.

The source for the compiler and tools must be obtained from the Rust repository or the standalone source tarballs.

rustup fails with Windows error 32

If rustup fails with Windows error 32, it may be due to antivirus scanning in the background. Disable antivirus scanner and try again.

I get "error: could not remove 'rustup-bin' file: 'C:\Users\USER\.cargo\bin\rustup.exe'"

If rustup fails to self-update in this way it's usually because RLS is running (your editor is open and running RLS). The solution is to stop RLS (by closing your editor) and try again.

rustup exited successfully but I can't run rustc --version

Restart your shell. This will reload your PATH environment variable to include Cargo's bin directory ($CARGO_HOME/bin).