Summary

Add a lightweight, opt-in propagation and tracing surface so context metadata
survives the process boundary (HTTP, gRPC, queues) and can be correlated
end-to-end.

Goal

Make the package observable and transportable across process boundaries without
turning it into a telemetry framework.

Problem

The context lives in AsyncLocal<T> and flows through await/Task within one
process, but it is lost at network boundaries (HTTP, gRPC, queues). There is no
simple, library-level way to write the current context into an outbound carrier
and rebuild it on the receiving side.

While the package now exposes the core serializer and propagator contracts
(IContextSerializer<T>, IContextPropagator<TCarrier>, ContextPayload),
there is no ready-made adapter for header carriers and no illustration of how
to rebuild context on the receiving side, so tracing an operation's flow across
services is awkward for:

• tracing
• auditing
• debugging
• integration with observability pipelines
• custom instrumentation in larger applications

Scope

• Add a header-based propagator adapter (e.g. X-Correlation-Id, X-Tenant-Id)
  built on IContextPropagator<TCarrier>.
• Add example(s) showing a client shipping context and a server middleware
  rebuilding it with BeginContext.
• Document the IContextPropagator/IContextSerializer usage against the new
  ContextPayload contract.
• Keep the tracing/Activity side as an observer (no change to the core
  execution path).

Design Expectations

• Propagation is opt-in and explicit; the library never auto-exports context.
• The propagator does not know the serializer or the concrete context type.
• The API focuses on observation/transport, not on policy.
• Consumers can ignore the propagation layer entirely.
• Context stays immutable; tracing is built on lifecycle events, never on the
  context object.

Acceptance Criteria

• The package exposes a usable header-based propagator and round-trip example.
• The lifecycle observer receives the already-present Previous/Current
  transitions for correlation.
• Actor execution behavior stays unchanged when no propagator is registered.
• The model stays small, structured, and format-neutral.

Non-Goals

• No W3C traceparent/tracestate or B3 support in v1.
• No APM/OpenTelemetry-specific sink.
• No background event bus.
• No retry/persistence/compliance layer.
• No changes to the core runtime execution path.

Notes

This issue covers distributed propagation (cross-boundary correlation) only.
Full OpenTelemetry/APM integration is out of scope here.