feat: enhance auto mode service and UI components for branch handling and verification

- Added a new function to retrieve the current branch name in the auto mode service, improving branch management.
- Updated the `getRunningCountForWorktree` method to utilize the current branch name for accurate feature counting.
- Modified UI components to include a toggle for skipping verification in auto mode, enhancing user control.
- Refactored various hooks and components to ensure consistent handling of branch names across the application.
- Introduced a new utility file for string operations, providing common functions for text manipulation.

apps/ui/src/components/views/board-view/hooks/use-board-actions.ts

@@ -487,7 +487,15 @@ export function useBoardActions({
   const handleStartImplementation = useCallback(
     async (feature: Feature) => {
       // Check capacity for the feature's specific worktree, not the current view
-      const featureBranchName = feature.branchName ?? null;
+      // Normalize the branch name: if the feature's branch is the primary worktree branch,
+      // treat it as null (main worktree) to match how running tasks are stored
+      const rawBranchName = feature.branchName ?? null;
+      const featureBranchName =
+        currentProject?.path &&
+        rawBranchName &&
+        isPrimaryWorktreeBranch(currentProject.path, rawBranchName)
+          ? null
+          : rawBranchName;
       const featureWorktreeState = currentProject
         ? getAutoModeState(currentProject.id, featureBranchName)
         : null;
@@ -567,6 +575,7 @@ export function useBoardActions({
       handleRunFeature,
       currentProject,
       getAutoModeState,
+      isPrimaryWorktreeBranch,
     ]
   );