…56] (#5011)

### What Does This Do

Adds LLMObs `session_id` to the cross-service propagation set (`_dd.p.llmobs_sid`), so a downstream service's LLM spans inherit the `session_id` set on an upstream service's span. Mirrors the existing `ml_app` propagation and the dd-trace-py change in [dd-trace-py#18952](DataDog/dd-trace-py#18952).

### Changes

- `internal/llmobs/context.go` — add `SessionID` to `PropagatedLLMSpan`.
- `internal/llmobs/span.go` — add `SessionID()` accessor; `propagatedSessionID` falls back to `s.propagated.SessionID` (mirrors `propagatedMLApp`).
- `ddtrace/tracer/span.go` — add `keyPropagatedLLMObsSessionID` (`_dd.p.llmobs_sid`); inject the active span's resolved session in `setLLMObsPropagatingTags` (only when non-empty, to conserve `x-datadog-tags` budget).
- `ddtrace/tracer/context.go` — extract `_dd.p.llmobs_sid` in `propagatedLLMSpanFromTags`.

The tag key `_dd.p.llmobs_sid` matches the wire contract agreed across SDKs (dd-trace-py, dd-trace-js): the `llmobs_` namespace is kept (consistent with `_dd.p.llmobs_parent_id` / `_ml_app` / `_trace_id`) while `session_id` is shortened to `sid` to conserve the `x-datadog-tags` budget.

An explicit `session_id` on a span still takes precedence over a propagated one.

### Scope note

This PR is **cross-service propagation only**. It does **not** add the in-process "trace-level default" (a sibling under a session-less parent inheriting the trace's session), which py/js get via their trace-shared propagating bag. In go, `internal/llmobs` can't reach the tracer's trace-level propagating tags (one-way import boundary), so a trace default would need a separate trace-scoped store with lifecycle management — deferred as a follow-up. Go already covers the common case (session on the root span → all descendants inherit via the parent-chain walk).

### Testing

[Simulating a distributed session](https://github.com/ncybul/sdk-manual-testing/blob/master/go/cross_service.go) ([trace](https://app.datadoghq.com/llm/traces?query=%40ml_app%3Asdk-manual-testing%20%40event_type%3Aspan%20%40parent_id%3Aundefined&agg_m=count&agg_m_source=base&agg_t=count&fromUser=false&is_llm_session=false&refresh_mode=sliding&selectedTab=overview&sp=%5B%7B%22p%22%3A%7B%22eventId%22%3A%22AwAAAZ9b5TBDrCwCXwAAABhBWjliNVRCREFBQVZqSm10cEJZZUFBQUEAAAAkZjE5ZjViZTgtNWVmNy00YThlLTk5ZTEtNGUzNzllYTJjYzVkAAForA%22%7D%2C%22i%22%3A%22llm-obs-panel%22%7D%5D&spanId=7720399594986875361&start=1783952628955&end=1783953528955&paused=false))

- `session_id:my-session` set in service A which calls service B and inherits the same session ID

[Simulating session inheritance in a trace unless explicitly annotated](https://github.com/ncybul/sdk-manual-testing/blob/master/go/in_process.go) ([trace](https://app.datadoghq.com/llm/traces?query=%40ml_app%3Asdk-manual-testing%20%40event_type%3Aspan%20%40parent_id%3Aundefined&agg_m=count&agg_m_source=base&agg_t=count&fromUser=false&is_llm_session=false&refresh_mode=sliding&selectedTab=overview&sp=%5B%7B%22p%22%3A%7B%22eventId%22%3A%22AwAAAZ9b6iswjqdBewAAABhBWjliNmlzd0FBQlMyTmJ0U0pfSEFBQUEAAAAkZjE5ZjViZWEtN2MzOS00MThkLTlkYjgtYmE3ZWIxZTMxNGY2AAAm-w%22%7D%2C%22i%22%3A%22llm-obs-panel%22%7D%5D&spanId=6028805347540461692&start=1783952718901&end=1783953618901&paused=false))

- root span sets `session_id:my-session` which is inherited by its children spans except those explicitly annotated with `session_id:other-session`

MLOB-7756

Co-authored-by: kakkoyun <[email protected]>
Co-authored-by: nicole.cybul <[email protected]>

…56] (#18952)

This PR adds propagation support for the LLMObs `session_id` across distributed contexts. This PR also establishes the first seen `session_id` as the default for all subsequent spans in the trace.

Annotation contexts / explicit session tagging are still respected with the consequence that one trace can have multiple session IDs (this is the current accepted behavior).

## Description

<!-- Provide an overview of the change and motivation for the change -->

## Testing

[Simulating a distributed session](https://github.com/ncybul/sdk-manual-testing/blob/master/cross_service.py) ([trace](https://app.datadoghq.com/llm/traces?query=%40ml_app%3Asdk-manual-testing%20%40event_type%3Aspan%20%40parent_id%3Aundefined&agg_m=count&agg_m_source=base&agg_t=count&fromUser=false&is_llm_session=false&refresh_mode=sliding&selectedTab=overview&sp=%5B%7B%22p%22%3A%7B%22eventId%22%3A%22AwAAAZ9Her5LhIWFvQAAABhBWjlIZXI1TEFBQUhjUkhSTTROd0FBQUEAAAAkMDE5ZjQ3N2EtZjJmYy00ZThhLWI1OTYtN2U0M2U3NDI0YmFhAAAF4w%22%7D%2C%22i%22%3A%22llm-obs-panel%22%7D%5D&spanId=1706347288156013108&start=1783607073040&end=1783610673040&paused=false))
- `session_id:my-session` set in service A which calls service B and inherits the same session ID

[Simulating default session being applied to subsequent spans in a trace unless explicitly annotated](https://github.com/ncybul/sdk-manual-testing/blob/master/in_process.py) ([trace](https://app.datadoghq.com/llm/traces?query=%40ml_app%3Asdk-manual-testing%20%40event_type%3Aspan%20%40parent_id%3Aundefined&agg_m=count&agg_m_source=base&agg_t=count&fromUser=false&is_llm_session=false&refresh_mode=sliding&selectedTab=overview&sp=%5B%7B%22p%22%3A%7B%22eventId%22%3A%22AwAAAZ9Hf--jl2WBRQAAABhBWjlIZi0takFBQ19vQ0UyalFQX0FBQUEAAAAkMDE5ZjQ3ODAtMDRiMC00NGVlLTk0MTgtN2VlNDdkMDc5ZDcwAAADRw%22%7D%2C%22i%22%3A%22llm-obs-panel%22%7D%5D&spanId=9624447665336394777&start=1783610133070&end=1783611033070&paused=false))
- first span sets `session_id:my-session` which is inherited by subsequent spans except those explicitly annotated with `session_id:other-session`

## Risks

<!-- Note any risks associated with this change, or "None" if no risks -->

## Additional Notes

<!-- Any other information that would be helpful for reviewers -->


Co-authored-by: nicole.cybul <[email protected]>