Move the duplicated test doubles into tests/Shared #755

The same hand-rolled fakes are declared in up to fifteen files each across the test projects, two clock approaches coexist, and tests/Shared holds a single file. Found in the 2026-09-27 repository review.

Context

Counts from grep -rl "class <Name>" tests:

• StubGitHubClient in 14 files, StubProbe in 15, SettingsRenderContext in 12, InMemoryTaskRepository in 9, StubAzureFoundryChatClient in 6, RecordingHandler in 5 files across 3 projects, StubHttpMessageHandler in 2 projects (Capture, Sync), RecordingTelemetry in 2 projects.
• Clocks: FixedClock in 11 files across 4 projects versus FakeTimeProvider in 45 files.
• tests/Shared holds only RepositoryRoot.cs, linked into every project by tests/Directory.Build.props; only Backlog.UI.Components.UnitTests has a Harnesses/ folder.
• Duplicate test class names make TRX and -class filters ambiguous: RenameRepositoryTests exists in both the Inbox and Tasks projects, MarkdownPreviewTests twice.
• Six near-identical assertion-free "Forgetting when nothing was stored is not an error" tests in tests/Backlog.Infrastructure.FileSystem.UnitTests/*CacheTests.cs lines 142 to 274 and Backlog.Infrastructure.Claude.UnitTests/ClaudeCodeUsageCacheTests.cs line 152.
• Polling helpers with bare Task.Delay(50) and DateTime.UtcNow deadlines in TasksDetailPaneTests.cs line 296, TasksWrittenElsewhereTests.cs line 140, RoadmapBandPaceTests.cs line 444; because they sit in private helpers, xUnit1051 never fires.

1. Move each double to tests/Shared/TestDoubles/<Name>.cs, linked the way RepositoryRoot.cs is, and delete the copies; where copies differ, keep the superset and add the behaviour switch as a constructor argument.
2. Standardise on FakeTimeProvider; delete FixedClock.
3. Add one WaitUntilAsync(Func<Task<bool>>) in tests/Shared that takes TestContext.Current.CancellationToken, and replace the three hand-rolled polls.
4. Prefix the duplicate class names with their context; wrap the assertion-free tests in Record.Exception with Assert.Null so intent is visible.

Route through delivery:flow-code per CLAUDE.md.