docs: the task-based state machines keep the trace context

content/en/documentation/for-adopters/control-plane/task-based-state-machines/_index.md

@@ -128,8 +128,8 @@ How to size workers, prefetch and the database pool is described in [Tuning](../
 
 Each subscriber contributes a liveness check, which fails when it stopped consuming (see
 [Health checks](../../observability/_index.md#health-checks)). The tasks pending in NATS can be inspected with the NATS
-tools, e.g. `nats consumer info tp-stream tp-subscriber`. The trace context of a negotiation or transfer process is not
-carried over to its tasks yet, so each task starts a new trace.
+tools, e.g. `nats consumer info tp-stream tp-subscriber`. Each task is processed within the trace context of its
+negotiation or transfer process, so all its steps belong to the trace in which it was created.
 
 ## Related
 

content/en/documentation/for-adopters/observability/_index.md

@@ -358,8 +358,8 @@ java -javaagent:opentelemetry-javaagent.jar \
 The agent traces the incoming and outgoing HTTP requests (Jetty, Jersey, OkHttp) and the database calls, and EDC adds
 spans for the incoming DSP messages, the processing of the contract negotiation and transfer process states, and the
 negotiations started through the Management API. The trace context of a negotiation or transfer is stored with it, so
-that its later steps belong to the same trace with the poll-based state machines; the task-based state machines don't
-carry it over yet. Events published to NATS carry the trace context of the step that emitted them.
+that its later steps belong to the same trace, with both the poll-based and the task-based state machines. Events
+published to NATS carry the trace context of the step that emitted them.
 
 Tracing has a cost: in load tests, the agent with full instrumentation reduced the throughput of the control plane
 noticeably. Sample traces (`otel.traces.sampler`) in production.