fix: support pg_stat_statements in extensions schema (Supabase)

Summary

  • Fix monitoring user access to pg_stat_statements on Supabase (and other providers that install extensions in a separate schema)
  • Auto-detect extension schema and grant USAGE if needed
  • Add extensions to search_path (harmless if schema doesn't exist)

Changes

  • 03.permissions.sql: Add DO block that detects pg_stat_statements schema and grants USAGE dynamically
  • init.ts: Update verification to check extension schema access and search_path
  • init.test.ts: Add tests for the new behavior

Test plan

  • Unit tests pass
  • Test on Supabase database with prepare-db
  • Verify monitoring user can query pg_stat_statements

🤖 Generated with Claude Code

Issue: https://gitlab.com/postgres-ai/platform/-/issues/346

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