feat(FN-2944): merge fusion/fn-2944

- test(FN-2944): cover already checked out worktree conflict recovery
- fix(FN-2944): recognize git already checked out worktree conflict
- fix(engine): auto-recover from squash-merge orphan rebase failures

Fusion-Task-Id: FN-2944

packages/dashboard/app/utils/pathDisplay.ts

@@ -0,0 +1,92 @@
+export interface PathBreadcrumb {
+  label: string;
+  path: string;
+}
+
+export function normalizeDisplayPath(path: string): string {
+  return path.replace(/\\/g, "/");
+}
+
+function trimTrailingSeparators(path: string): string {
+  return path.replace(/[\\/]+$/g, "");
+}
+
+export function splitPathSegments(path: string): string[] {
+  const normalized = normalizeDisplayPath(trimTrailingSeparators(path));
+  if (!normalized) return [];
+  return normalized.split("/").filter(Boolean);
+}
+
+export function getPathBasename(path: string): string {
+  const normalized = normalizeDisplayPath(trimTrailingSeparators(path));
+  if (!normalized) return path;
+  const segments = normalized.split("/").filter(Boolean);
+  return segments[segments.length - 1] || normalized;
+}
+
+export function getTrailingPath(path: string, count: number): string {
+  const segments = splitPathSegments(path);
+  if (segments.length === 0) {
+    return normalizeDisplayPath(path);
+  }
+  return segments.slice(-count).join("/");
+}
+
+export function getDisplayDirname(path: string): string {
+  const normalized = normalizeDisplayPath(trimTrailingSeparators(path));
+  const lastSeparator = normalized.lastIndexOf("/");
+  if (lastSeparator < 0) return "";
+  return normalized.slice(0, lastSeparator + 1);
+}
+
+export function joinDisplayPath(basePath: string, name: string): string {
+  if (!basePath || basePath === ".") {
+    return name;
+  }
+  const segments = splitPathSegments(basePath);
+  return [...segments, name].join("/");
+}
+
+export function getParentDisplayPath(path: string): string {
+  const segments = splitPathSegments(path);
+  if (segments.length === 0) {
+    return ".";
+  }
+  segments.pop();
+  return segments.length === 0 ? "." : segments.join("/");
+}
+
+export function getPathBreadcrumbs(path: string): PathBreadcrumb[] {
+  const normalized = normalizeDisplayPath(path);
+  const winMatch = normalized.match(/^([A-Za-z]:)(?:\/(.*))?$/);
+  if (winMatch) {
+    const root = `${winMatch[1]}/`;
+    const segments = (winMatch[2] ?? "").split("/").filter(Boolean);
+    const breadcrumbs: PathBreadcrumb[] = [{ label: winMatch[1], path: root }];
+    for (let i = 0; i < segments.length; i += 1) {
+      breadcrumbs.push({
+        label: segments[i]!,
+        path: `${root}${segments.slice(0, i + 1).join("/")}`,
+      });
+    }
+    return breadcrumbs;
+  }
+
+  if (normalized.startsWith("/")) {
+    const segments = normalized.split("/").filter(Boolean);
+    const breadcrumbs: PathBreadcrumb[] = [{ label: "/", path: "/" }];
+    for (let i = 0; i < segments.length; i += 1) {
+      breadcrumbs.push({
+        label: segments[i]!,
+        path: `/${segments.slice(0, i + 1).join("/")}`,
+      });
+    }
+    return breadcrumbs;
+  }
+
+  const segments = normalized.split("/").filter(Boolean);
+  return segments.map((segment, index) => ({
+    label: segment,
+    path: segments.slice(0, index + 1).join("/"),
+  }));
+}

packages/dashboard/app/utils/worktreeGrouping.ts

@@ -1,4 +1,5 @@
 import type { Task } from "@fusion/core";
+import { getPathBasename } from "./pathDisplay";
 
 export interface WorktreeGroupData {
   label: string;
@@ -11,9 +12,7 @@ export interface WorktreeGroupData {
  * e.g. ".worktrees/FN-001" → "FN-001", "/path/to/fn/fn-001" → "fn-001"
  */
 export function getWorktreeLabel(worktreePath: string): string {
-  // Take the last segment of the path
-  const segments = worktreePath.replace(/\/+$/, "").split("/");
-  return segments[segments.length - 1] || worktreePath;
+  return getPathBasename(worktreePath) || worktreePath;
 }
 
 /**