[Backend] Cover archived-board skip recovery

[Chris0Jeky]

Summary

• add the missing application-service regression for archived-board skip counts recovering from nonzero to zero
• keep a real expirable proposal in the second sweep so the test proves expiry, persistence, notification, and logging together
• leave the DI lifetime, worker, repository, and canonical STATUS decisions out of this test-only slice

Verification

• baseline edge-case class: 15 passed, 0 skipped
• focused new regression: 1 passed, 0 skipped
• final dotnet test backend/tests/Taskdeck.Application.Tests/Taskdeck.Application.Tests.csproj -c Release -m:1 --filter "FullyQualifiedName~Taskdeck.Application.Tests.Services.AutomationProposalServiceEdgeCaseTests": 16 passed, 0 skipped
• git diff --check: passed
• two coordinator review passes: no blocking findings

The test-only change is a regression guard for behavior already present in production code; it is not claimed as a pre-fix bug proof. The broader solution gate and hosted checks remain pending. Automatic Codex review is unavailable because the account review quota is exhausted.

Refs #2520

[chatgpt-codex-connector]

You have reached your Codex usage limits for code reviews. You can see your limits in the Codex usage dashboard.
To continue using code reviews, add credits to your account and enable them for code reviews in your settings.