asdf rust triggers warnings when installing rust versions

### Provide environment information

```bash
$ asdf info
OS:
Darwin najma.local 24.3.0 Darwin Kernel Version 24.3.0: Thu Jan 2 20:24:16 PST 2025; root:xnu-11215.81.4~3/RELEASE_ARM64_T6000 arm64

SHELL:
zsh 5.9 (arm64-apple-darwin24.0)

BASH VERSION:
5.2.32(1)-release

ASDF VERSION:
0.16.2

ASDF INTERNAL VARIABLES:
ASDF_DEFAULT_TOOL_VERSIONS_FILENAME=.tool-versions
ASDF_DATA_DIR=/Users/andrew/.asdf
ASDF_CONFIG_FILE=/Users/andrew/.asdfrc

ASDF INSTALLED PLUGINS:
golang https://github.com/kennyp/asdf-golang.git cc8bc47d4877beed61e10815d46669e1eaaa0bbe
gradle https://github.com/rfrancis/asdf-gradle.git 4adbc6f46837a487d9b04b4e0c681134f74710d5
java https://github.com/halcyon/asdf-java.git dcc991a7170e5160bdb0f9c058d1648a3094e10c
nodejs https://github.com/asdf-vm/asdf-nodejs.git 65441d3752992176c10800ef8bf898b864397978
python https://github.com/danhper/asdf-python.git 8505457c6612514688ba473386d2063d4c83bb54
ruby https://github.com/asdf-vm/asdf-ruby.git 28333230752fa8b271c1f3b95b68fb3af3069a66
rust https://github.com/code-lever/asdf-rust.git 0c88f995dc3032b2ab1774076606f65b1a43328f
```

### To Reproduce

```console
$ asdf install
info: downloading installer
warn: It looks like you have an existing installation of Rust at:
warn: /Users/andrew/.asdf/shims
warn: It is recommended that rustup be the primary Rust installation.
warn: Otherwise you may have confusion unless you are careful with your PATH.
warn: If you are sure that you want both rustup and your already installed Rust
warn: then please reply `y' or `yes' or set RUSTUP_INIT_SKIP_PATH_CHECK to yes
warn: or pass `-y' to ignore all ignorable checks.
error: cannot install while Rust is installed
warn: continuing (because the -y flag is set and the error is ignorable)
...
```

### Describe the Bug

asdf-rust fails to quiet Rust installer warnings triggered by the very common scenario that the user already has another (asdf-)rust version installed.

### Expected Behaviour

asdf-rust automatically applies the documented RUSTUP_INIT_SKIP_PATH_CHECK environment variable to child processes.

Start at the asdf-rust installation entry point used by `asdf install` and inspect how the Rust installer is invoked. Review the documented `RUSTUP_INIT_SKIP_PATH_CHECK` behavior and verify the environment reaches child processes. Done means installing Rust no longer emits the existing-installation warnings in this scenario.

Written by the indexing model from the issue text.