feat(llmobs): prompt management SDK methods

[PROFeNoM]

Description

Adds prompt management methods to the LLMObs Python SDK, calling the new public API endpoints from MLOB-7523.

Blocked by: https://github.com/DataDog/dd-source/pull/443753 (public CRUD API routes)

New public API

# Write methods (require DD_API_KEY + DD_APP_KEY)
LLMObs.create_prompt(prompt_id, template, *, title, description, user_version, labels)
LLMObs.create_prompt_version(prompt_id, template, *, description, user_version, labels)
LLMObs.update_prompt(prompt_id, *, title, description)
LLMObs.update_prompt_version(prompt_id, version, *, labels, description)
LLMObs.delete_prompt(prompt_id)

# Read methods (require DD_API_KEY only)
LLMObs.list_prompts(*, ml_app)
LLMObs.list_prompt_versions(prompt_id)

Not covered: GET /prompts/{prompt_id}/versions/{version} is intentionally left out. Prefer to add it once #18127 (hybrid prompt delivery) lands, since it changes the get_prompt signature - at that point we can decide whether to add version= as an optional parameter to get_prompt rather than a separate method.

New types (ddtrace/llmobs/types.py)

• PromptLabel = Literal["development", "production"] - allowed label values
• ChatMessage(TypedDict) - template message format (role + content only)
• PromptResponse(TypedDict) - returned by create/update/list prompt operations
• PromptVersionResponse(TypedDict) - returned by create/update/list version operations
• DeletedPromptResponse(TypedDict) - returned by delete

Exception hierarchy

PromptAPIError (base)
  PromptAuthError        - 401/403 (bad API/app key)
  PromptValidationError  - 400 (bad input)
  PromptNotFoundError    - 404
  PromptConflictError    - 409 (duplicate prompt_id)
  PromptServerError      - 5xx

Each method documents which exceptions it can raise.

Cache changes (cache.py)

• WarmCache now uses per-prompt subdirectories: ~/.cache/datadog/llmobs/prompts/{prompt_id}/{label}.json
• Added evict_prompt(prompt_id) - uses shutil.rmtree on the prompt directory
• Previous flat-file layout had prefix collision bugs (e.g., deleting "greeting" could evict "greeting-v2" cache entries)

Files changed

File	Change
types.py	PromptLabel, ChatMessage, 3 response TypedDicts, 5 exception classes
cache.py	Per-prompt subdirectory layout, evict_prompt method
manager.py	_request helper, 7 CRUD methods, API key validation on get_prompt
_llmobs.py	7 public classmethods delegating to manager
test_prompts.py	Exception mapping test, cache eviction test

[datadog-prod-us1-6]

🎉 All green!

🧪 All tests passed
❄️ No new flaky tests detected

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[cit-pr-commenter-54b7da]

Codeowners resolved as

ddtrace/llmobs/_prompts/manager.py                                      @DataDog/ml-observability