Sync LLM Observability API documentation with Go implementation

[aniszoubiramar]

Updated API documentation to match the current Go implementation (source of truth). Applied 90 changes across 15 endpoints in 2 documentation files.

Summary by Endpoint

Endpoint	Changes
POST /api/intake/llm-obs/v1/trace/spans	18 changes
GET /api/v2/llm-obs/v1/{project_id}/datasets	15 changes
GET /api/v2/llm-obs/v1/{project_id}/datasets/{dataset_id}/records	14 changes
POST /api/v2/llm-obs/v1/experiments/{experiment_id}/events	11 changes
POST /api/intake/llm-obs/v2/eval-metric	10 changes
GET /api/v2/llm-obs/v1/experiments	7 changes
PATCH /api/v2/llm-obs/v1/projects/{project_id}	4 changes
POST /api/v2/llm-obs/v1/{project_id}/datasets/{dataset_id}/records	3 changes
GET /api/v2/llm-obs/v1/projects	2 changes
PATCH /api/v2/llm-obs/v1/experiments/{experiment_id}	2 changes
POST /api/v2/llm-obs/v1/projects	1 change
POST /api/v2/llm-obs/v1/projects/delete	1 change
POST /api/v2/llm-obs/v1/{project_id}/datasets	1 change
POST /api/v2/llm-obs/v1/experiments	1 change
POST /api/v2/llm-obs/v1/spans/events/search	1 change (structural)

Change Types

Type	Count
Fields added	76
Type fixes	3
Required status fixes	11
Total	90

Files Modified

• content/en/llm_observability/experiments/_index.md
• content/en/llm_observability/instrumentation/api.md

🤖 Generated with Claude Code

What does this PR do? What is the motivation?

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Modified Files

• https://docs-staging.datadoghq.com/anis.amar/llm-obs-api-sync-20260108-102412/llm_observability/experiments/
• https://docs-staging.datadoghq.com/anis.amar/llm-obs-api-sync-20260108-102412/llm_observability/instrumentation/api