fix(desktop): mirror Windows path identity in live overlay + WSL spelling

Addresses @teknium1's review of #61950:

- The desktop live overlay (workspace-groups.ts) matched cwd membership
  case-sensitively, so a fresh mixed-case/separator Windows session missed
  its explicit/auto project until the next backend tree refresh. Mirror the
  backend identity (isWindowsPath/comparisonSegments/pathKey) in isPathUnder,
  liveSessionProjectId, and overlayRepoLanes lane matching. Comparison-only —
  emitted ids/labels keep their spelling. POSIX stays case-sensitive.
- Backend _is_windows_path missed root-relative `\wsl.localhost\...` (single
  leading backslash), leaving that historical spelling case-sensitive. Classify
  any backslash-rooted path as Windows.

Tests: WSL-spelling collapse + explicit-project precedence (project_tree),
Windows/WSL live-overlay membership + POSIX case-sensitivity (workspace-groups).

apps/desktop/src/app/chat/sidebar/projects/workspace-groups.test.ts

@@ -494,6 +494,29 @@ describe('liveSessionProjectId', () => {
 
     expect(id).toBe('p_app')
   })
+
+  it('matches a mixed-case/separator Windows cwd to its explicit project in the live overlay', () => {
+    // The bug: a fresh Windows session drops into the overlay before the next
+    // backend refresh; case-sensitive matching missed its project until then.
+    const id = liveSessionProjectId(makeSession('c:/work/notes/SUB'), [makeProject('p_notes', ['C:\\Work\\Notes'])])
+
+    expect(id).toBe('p_notes')
+  })
+
+  it('matches a root-relative WSL cwd (single backslash) case-insensitively', () => {
+    const id = liveSessionProjectId(makeSession('//wsl.localhost/Ubuntu/home/alice/PROJ'), [
+      makeProject('p_proj', ['\\wsl.localhost\\Ubuntu\\home\\alice\\proj'])
+    ])
+
+    expect(id).toBe('p_proj')
+  })
+
+  it('keeps POSIX cwd matching case-sensitive (no false project match)', () => {
+    // Distinct case on POSIX is a distinct path → falls back to its own auto id.
+    expect(liveSessionProjectId(makeSession('/work/notes'), [makeProject('p_notes', ['/Work/Notes'])])).toBe(
+      '/work/notes'
+    )
+  })
 })
 
 describe('overlayLiveLanes', () => {

apps/desktop/src/app/chat/sidebar/projects/workspace-groups.ts

@@ -73,6 +73,27 @@ const segments = (path: string): string[] =>
 /** A path with trailing separators stripped, for stable equality checks. */
 const normalizePath = (path: null | string | undefined): string => (path ?? '').replace(/[/\\]+$/, '')
 
+// Windows spellings: drive-letter (`C:\…`), UNC (`\\srv`, `//srv`), or any
+// backslash-rooted path (`\wsl.localhost\…`). A single leading `/` stays POSIX.
+// Mirrors the backend `_is_windows_path` so the live overlay places rows into
+// the same project the backend tree would.
+const isWindowsPath = (path: string): boolean =>
+  /^[A-Za-z]:[/\\]/.test(path) || path.startsWith('\\') || path.startsWith('//')
+
+/**
+ * Segments for identity comparison: Windows paths fold case (and separators, via
+ * {@link segments}) so `C:\Work` and `c:/work` are one lane; POSIX stays
+ * case-sensitive. Comparison-only — emitted ids/labels keep their spelling.
+ */
+const comparisonSegments = (path: string): string[] => {
+  const segs = segments(path)
+
+  return isWindowsPath(path) ? segs.map(seg => seg.toLowerCase()) : segs
+}
+
+/** Canonical per-host comparison key (separator/case/trailing-slash agnostic). */
+const pathKey = (path: null | string | undefined): string => comparisonSegments(path ?? '').join('/')
+
 /** Last path segment. */
 export const baseName = (path: string): string | undefined => segments(path).pop()
 
@@ -317,8 +338,8 @@ export function mergeRepoWorktreeGroups(
 
 /** True when `target` equals `folder` or is nested under it (segment-wise). */
 function isPathUnder(folder: string, target: string): boolean {
-  const f = segments(folder)
-  const t = segments(target)
+  const f = comparisonSegments(folder)
+  const t = comparisonSegments(target)
 
   if (!f.length || f.length > t.length) {
     return false
@@ -347,9 +368,8 @@ export function liveSessionProjectId(session: SessionInfo, explicitProjects: Pro
 
   // No persisted repo root yet (brand-new session) → the cwd is the root.
   const repoRoot = (session.git_repo_root || '').trim() || cwd
-  const underRepo = cwd === repoRoot || cwd.startsWith(`${repoRoot}/`) || cwd.startsWith(`${repoRoot}\\`)
 
-  if (!underRepo) {
+  if (!isPathUnder(repoRoot, cwd)) {
     return null
   }
 
@@ -423,7 +443,7 @@ export function overlayRepoLanes(
   live: SessionInfo[],
   removed: ReadonlySet<string> = NO_REMOVED
 ): SidebarWorkspaceTree {
-  const repoRoot = normalizePath(repo.path)
+  const repoRootKey = pathKey(repo.path)
   let changed = false
 
   // Snapshot lanes minus anything the user just deleted/archived.
@@ -457,7 +477,7 @@ export function overlayRepoLanes(
     for (const g of lanes) {
       const lanePath = normalizePath(g.path)
 
-      if (!lanePath || lanePath === repoRoot || !isPathUnder(lanePath, cwd)) {
+      if (!lanePath || pathKey(lanePath) === repoRootKey || !isPathUnder(lanePath, cwd)) {
         continue
       }
 
@@ -480,14 +500,14 @@ export function overlayRepoLanes(
         continue
       }
 
-      const placedPath = normalizePath(placed.path)
+      const placedKey = pathKey(placed.path)
 
       lane =
         lanes.find(g => g.id === placed.id) ??
         (placed.isMain
           ? lanes.find(g => g.isMain && g.label.toLowerCase() === placed.label.toLowerCase())
           : undefined) ??
-        (!placed.isMain && placedPath ? lanes.find(g => normalizePath(g.path) === placedPath) : undefined)
+        (!placed.isMain && placedKey ? lanes.find(g => pathKey(g.path) === placedKey) : undefined)
 
       if (!lane) {
         lane = { ...placed, sessions: [] }

tests/tui_gateway/test_project_tree.py

@@ -237,6 +237,31 @@ def test_windows_path_identity_preserves_explicit_project_priority():
     assert tree["scoped_session_ids"] == [session["id"]]
 
 
+def test_wsl_localhost_cwds_collapse_into_one_auto_project():
+    # Root-relative WSL spellings (single leading backslash) are Windows paths,
+    # so case/separator variants collapse instead of spawning duplicate autos.
+    sessions = [
+        _session(r"\wsl.localhost\Ubuntu\home\alice\proj"),
+        _session("//wsl.localhost/Ubuntu/home/alice/PROJ"),
+    ]
+
+    tree = pt.build_tree([], sessions, [], resolve=lambda _cwd: None, hydrate=True)
+
+    assert len(tree["projects"]) == 1
+    assert tree["projects"][0]["sessionCount"] == 2
+
+
+def test_wsl_localhost_path_cannot_bypass_explicit_project():
+    explicit = _project("p_proj", "Proj", [r"\wsl.localhost\Ubuntu\home\alice\proj"])
+    session = _session("//wsl.localhost/Ubuntu/home/alice/PROJ/")
+
+    tree = pt.build_tree([explicit], [session], [], resolve=lambda _cwd: None, hydrate=True)
+
+    assert [p["id"] for p in tree["projects"]] == ["p_proj"]
+    assert tree["projects"][0]["sessionCount"] == 1
+    assert tree["scoped_session_ids"] == [session["id"]]
+
+
 def test_posix_path_identity_remains_case_sensitive():
     explicit = _project("p_notes", "Notes", ["/Work/Notes"])
     session = _session("/work/notes")

tui_gateway/project_tree.py

@@ -62,7 +62,10 @@ def _segments(path: str) -> list[str]:
 
 def _is_windows_path(path: str) -> bool:
     value = (path or "").strip()
-    return bool(re.match(r"^[A-Za-z]:[/\\]", value)) or value.startswith(("\\\\", "//"))
+    # Drive-letter (`C:\…`), UNC (`\\srv`, `//srv`), or any backslash-rooted path
+    # — the root-relative `\wsl.localhost\…` / `\Users\…` spellings included. A
+    # single leading `/` stays POSIX (case-sensitive).
+    return bool(re.match(r"^[A-Za-z]:[/\\]", value)) or value.startswith(("\\", "//"))
 
 
 def _comparison_segments(path: str) -> list[str]: