Run the database provider tests in CI against PostgreSQL

[Sev7eNup]

Closes the CI half of #379.

The DatabaseIntegration category covers the hand-written per-provider SQL — the atomic dispatch claim (FOR UPDATE SKIP LOCKED / UPDLOCK,READPAST,READCOMMITTEDLOCK), the consolidated InitialBaseline migration, startup recovery, and the dashboard duration trend with its three dialects. Each of those tests calls Assert.Skip without a server, and CI set neither NODEPILOT_TEST_POSTGRES nor NODEPILOT_TEST_SQLSERVER. So the PostgreSQL branch, which is the production default, was executed by nothing unless somebody remembered to start Docker locally.

The new database job starts the PostgreSQL the Windows runner already ships (installed, stopped, password root) and points the environment variable at it. Each fixture still creates its own nodepilot_test_<guid> database, so the admin connection only ever creates and drops those.

A job of its own rather than a step inside backend, so a database that fails to start reports as a database failure instead of hiding in the coverage run. It is wired into ci-gate and follows the same changes.code condition as the other code jobs.

SQL Server is not on the Windows image, so its InlineData cases keep skipping and stay a local concern through scripts/Test-DatabaseProviders.ps1. CONTRIBUTING.md says so where the script is documented.