[BUG] Checkpoint worktree path comparison fails on Windows due to path identity mismatch

[0xMink]

Description

ShadowCheckpointService.initShadowGit() compares core.worktree to this.workspaceDir using raw string equality (worktree !== this.workspaceDir at ~line 158). On Windows, equivalent paths can differ in string representation, causing checkpoints to fail with:

Checkpoints can only be used in the original workspace: C:/Users/Foo/project !== C:\Users\Foo\project

Root cause

Git on Windows stores core.worktree with forward slashes (e.g., C:/Users/Foo/project), while VS Code resolves workspace paths with native backslashes (e.g., C:\Users\Foo\project). Additional divergence sources include:

• Drive-letter casing: c:\project vs C:\project
• Trailing separators: C:\project\ vs C:\project
• Symlink resolution: realpath may differ from the originally-provided path

How to reproduce

1. Open a workspace on Windows where the workspace path uses backslashes
2. Create a task that initializes checkpoints (shadow git repo is created, core.worktree stored with forward slashes)
3. Close and reopen the workspace (VS Code may resolve the path differently)
4. Attempt to resume the task — checkpoint initialization fails because core.worktree (forward slashes) doesn't string-match workspaceDir (backslashes)

Search pattern

worktree !== this.workspaceDir

Suggested fix

Add a normalizePathForCompare() helper that:

• Applies path.resolve() + path.normalize() to canonicalize separators
• Strips trailing path separators
• Uses case-insensitive comparison on win32 platform
• Preserves fail-closed behavior: missing/undefined core.worktree still throws

Acceptance criteria

• Equivalent Windows paths with different separator styles are recognized as equal
• Drive-letter casing differences don't cause false mismatches
• Trailing separator differences don't cause false mismatches
• Missing core.worktree still throws (fail-closed preserved)
• No behavioral change on macOS/Linux (paths are already case-sensitive and use consistent separators)

[roomote]

I've analyzed this issue and here's my proposed implementation plan:

The codebase already has an arePathsEqual() utility in src/utils/path.ts that handles all the cases described in this issue:

• Uses path.normalize() to canonicalize separators (forward slash vs backslash)
• Strips trailing path separators
• Case-insensitive comparison on win32 platform
• Returns false when either argument is undefined/empty (fail-closed)

The fix is a two-line change in src/services/checkpoints/ShadowCheckpointService.ts:

1. Add import: Import arePathsEqual from ../../utils/path
2. Replace raw comparison at line 158: Change worktree !== this.workspaceDir to !arePathsEqual(worktree, this.workspaceDir)

No new helper function is needed since arePathsEqual already covers all the acceptance criteria. Existing tests in src/utils/__tests__/path.spec.ts already validate the cross-platform behavior. I'll also add a unit test to the existing ShadowCheckpointService.spec.ts to verify the worktree comparison specifically uses normalized path comparison.

Please mention @roomote in a comment saying that you approve this plan, and I'll proceed with the implementation.