diag: run backend suite after #22 + #27 fixes (#14)

[fxbin]

Diagnostic-only integration PR for #14. CLOSED WITHOUT MERGE.

Evidence mission completed:

• composed the verified [P0][Test Isolation] Admin permission test leaks real DuckDB PostgreSQL attach and blocks next clean_tables TRUNCATE #22 and [P0][Test Isolation] Fixture setup hangs after content favorite test before content pipeline test #27 isolation fixes only in the Actions workspace;
• collected 817 backend tests and progressed through ~38% within the bounded 180-second diagnostic window;
• confirmed the original 0%/19% cross-test hang boundaries were passed;
• exposed the next regression clusters, including the Analysis/Recovery/Post-sync set now decomposed under [P0] Stabilize analysis recovery, inflight dedup and post-sync drain regressions #35/[P1] Align analysis/notification permission regression test with admin-only analysis trigger contract #37/[P1] Migrate post-sync drain regression tests to the extracted pipeline module #39/[P0] Isolate analysis-job persistence from pytest event-loop reuse #40.

No composed diagnostic state is intended for production history.

Artifact-boundary verdict: process-only → closed, not merged.