Document targeting rule permission requirements

[emielver]

What does this PR do? What is the motivation?

Documents the permission requirements for feature flag targeting-rule allocation operations:

• Feature Flag Write is the baseline permission.
• Product Analytics Experiments Write is also required for experiment-owned allocation state, including existing state during full-set replacements.

Updates the API reference metadata, the targeting-rules concept page, and the affected MCP tool entries.

Merge readiness

• Ready for merge

AI assistance

Used Codex to audit the permission references, draft the updates, and run validation.

Additional notes

Validation completed:

• Vale on changed lines
• OpenAPI YAML parse with the repository JavaScript parser
• Translation JSON parse with jq
• git diff --check

[github-actions]

Preview links (active after the build_preview check completes)

Modified Files

• https://docs-staging.datadoghq.com/emiel.verkade/document-feature-flag-experiment-permissions/feature_flags/concepts/targeting_rules
• https://docs-staging.datadoghq.com/emiel.verkade/document-feature-flag-experiment-permissions/mcp_server/tools