Fix stale published run status

[AbigailDeng]

Problem

A published run can be completed in its run audit while the member run catalog still returns the older running summary. The selected run then showed Completed in the detail pane but Running in the published-runs list.

Solution

Use the audit summary only when it belongs to the currently selected runId, and use that summary to replace the matching catalog item. This keeps the detail pane and left-hand run list on the same current status while avoiding stale data from a previous route selection.

The branch is merged with feat/2026-08-04_workflow-activity-vnext, which is also the PR base.

Local verification

• Related tests: pnpm --dir apps/aevatar-console-web exec jest src/pages/runtime-published-runs/index.test.tsx --runInBand (8 passed)
• Related tests: pnpm --dir apps/aevatar-console-web exec jest --findRelatedTests src/pages/runtime-published-runs/MemberPublishedRunsReplay.tsx --runInBand (8 passed)
• Stability guard: bash tools/ci/test_stability_guards.sh (passed)
• Changed-file static check: pnpm --dir apps/aevatar-console-web exec biome lint --only=suspicious/noExplicitAny src/pages/runtime-published-runs/MemberPublishedRunsReplay.tsx src/pages/runtime-published-runs/index.test.tsx (passed)
• Full changed-file Biome check: reports pre-existing target-branch diagnostics for quote formatting/import order, noArrayIndexKey, and noNonNullAssertion; no whole-file formatting was applied
• Diff check: git diff origin/feat/2026-08-04_workflow-activity-vnext --check -- apps/aevatar-console-web/src/pages/runtime-published-runs/MemberPublishedRunsReplay.tsx apps/aevatar-console-web/src/pages/runtime-published-runs/index.test.tsx (passed)
• Full frontend suite/build: deferred to GitHub CI by personal local workflow policy