Callback on context change

Why you need this feature?

Elastic is proposing a donation of our continuous profiler (https://github.com/open-telemetry/community/issues/1918). In order to do correlation of profiling data with traces collected by language sdks we need to provide to the profiler current thread trace id, span id and root span id.

Describe the solution you'd like

Following java implementation I thought an hook on the context api may work, I've done a quick POC here:

https://gist.github.com/xrmx/fc81e710e7a860ca229839b10e780dfd

On the technical side I'm unsure if the optional hook callback should be configured via an environment variable or via an entrypoint.

Describe alternatives you've considered

An alternative if the context is the right place to hook would be to provide a custom context storage implementation but that would not be generic or upstreamable.

Additional context

In the java sdk they have https://javadoc.io/doc/io.opentelemetry/opentelemetry-context/latest/io/opentelemetry/context/ContextStorage.html#addWrapper(java.util.function.Function)

Start by reviewing the context API and the linked Python proof of concept, then compare the proposed hook with Java's ContextStorage.addWrapper implementation. The issue needs a decision on the callback design and whether configuration uses an environment variable or an entrypoint; done means an agreed, generic upstreamable approach for exposing current trace context to the profiler.