[DBM Doc] Document new agent diagnose support for Postgres DBM setup

[pierreln-dd]

Confidence: DISCUSSION

Source PR: DataDog/integrations-core#23433

What changed:
The Postgres integration now surfaces common DBM setup issues via datadog-agent diagnose. The new diagnostic framework validates:

• Connection and authentication
• Postgres version support
• Server GUCs: shared_preload_libraries, track_activity_query_size, track_io_timing, pg_stat_statements.max
• pg_monitor role membership
• Access to pg_stat_activity, pg_stat_database, pg_stat_statements
• Per-database datadog schema, pg_stat_statements extension, and datadog.explain_statement function

Diagnostics are gated on the DBM subfeatures that require each dependency (e.g., query_metrics checks shared_preload_libraries, query_samples validates the explain function) and cascade-suppress so a single root cause yields one actionable diagnostic.

Why document this:
Users can now run datadog-agent diagnose to validate their Postgres DBM setup and get actionable remediation hints for common configuration issues. The self-hosted setup guide should mention this diagnostic capability so users know they can validate their configuration after completing the setup steps.

Uncertainty:
The PR does not explicitly state a minimum Agent version for the new diagnostics, though the code changes are in integrations-core only. The placement and wording of the diagnostic callout in the setup flow is open to discussion — should it go near "Verify database permissions" or as a separate troubleshooting step?

[github-actions]

Preview links (active after the build_preview check completes)

Modified Files

• https://docs-staging.datadoghq.com/pierreln-dd/dbm-doc-postgres-23433-1781634365/database_monitoring/setup_postgres/selfhosted