fix(llmobs): properly parse DD_TAGS onto span events' tags [backport 3.12] (#14322)

Backport 8ac5581 from #14320 to 3.12.

Properly parse `DD_TAGS` onto the llmobs span events' tags field.

### Manual testing
Running `DD_TAGS="foo:bar,buz:bax" python test.py` against
```python
from ddtrace.llmobs import LLMObs
LLMObs.enable(ml_app="sam-test")

with LLMObs.workflow(name="test"):
    pass
```
gives the following tags on the span event
<img width="1386" height="106" alt="Screenshot 2025-08-15 at 2 48 57 PM"
src="https://github.com/user-attachments/assets/32ac31e0-ab79-46c2-9ad5-5a99b4fa8bd5"
/>


## Checklist
- [x] PR author has checked that all the criteria below are met
- The PR description includes an overview of the change
- The PR description articulates the motivation for the change
- The change includes tests OR the PR description describes a testing
strategy
- The PR description notes risks associated with the change, if any
- Newly-added code is easy to change
- The change follows the [library release note
guidelines](https://ddtrace.readthedocs.io/en/stable/releasenotes.html)
- The change includes or references documentation updates if necessary
- Backport labels are set (if
[applicable](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting))

## Reviewer Checklist
- [x] Reviewer has checked that all the criteria below are met 
- Title is accurate
- All changes are related to the pull request's stated goal
- Avoids breaking
[API](https://ddtrace.readthedocs.io/en/stable/versioning.html#interfaces)
changes
- Testing strategy adequately addresses listed risks
- Newly-added code is easy to change
- Release note makes sense to a user of the library
- If necessary, author has acknowledged and discussed the performance
implications of this PR as reported in the benchmarks PR comment
- Backport labels are set in a manner that is consistent with the
[release branch maintenance
policy](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting)

Co-authored-by: Sam Brenner <[email protected]>

Author: dd-octo-sts[bot]

ddtrace/llmobs/_llmobs.py

@@ -409,7 +409,9 @@ def _llmobs_span_event(self, span: Span) -> Optional[LLMObsSpanEvent]:
 
     @staticmethod
     def _llmobs_tags(span: Span, ml_app: str, session_id: Optional[str] = None) -> List[str]:
+        dd_tags = config.tags
         tags = {
+            **dd_tags,
             "version": config.version or "",
             "env": config.env or "",
             "service": span.service or "",

releasenotes/notes/llmobs-add-dd-tags-f2203cb49cb531af.yaml

@@ -0,0 +1,4 @@
+---
+fixes:
+  - |
+    LLM Observability: Properly parse ``DD_TAGS`` onto LLM Observability span events' tags.