[Feature]: Support the environment variable propagation spec in Rust

[adrielp]

Related Problems?

With the environment variable context propagation spec being added, we'd like to have its support added to Javascript. This is part of a larger effort to adding support in each of the currently supported languages.

Describe the solution you'd like:

I'd like the specification implemented in Rust.

Considered Alternatives

n/a

Additional Context

No response

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