[feature request] Support the environment variable propagation spec in dotnet

[adrielp]

Package

OpenTelemetry.Extensions.Propagators

Is your feature request related to a problem?

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

What is the expected behavior?

That users of DotNet are able to propagate context through environment carriers.

Which alternative solutions or features have you considered?

n/a

Additional context

No response

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[pellared]

This is already Beta and undergoing stabilization:

• Stabilize "Environment Variables as Context Propagation Carriers" document opentelemetry-specification#5040

It would be very helpful if someone could try to implement this.

[martincostello]

I'll mark this as help wanted for now, but if no one picks it up I'll have a look into it.

[martincostello]

Note to implementer: when completed, add a link to Environment Variables as Context Propagation Carriers > Supplementary Guidelines.

[martincostello]

Draft up at #7174 - feedback welcome.