fix: Complete fix for plan mode system across all providers

Closes #671 (Complete fix for the plan mode system inside automaker)
Related: #619, #627, #531, #660

## Issues Fixed

### 1. Non-Claude Provider Support
- Removed Claude model restriction from planning mode UI selectors
- Added `detectSpecFallback()` function to detect specs without `[SPEC_GENERATED]` marker
- All providers (OpenAI, Gemini, Cursor, etc.) can now use spec and full planning modes
- Fallback detection looks for structural elements: tasks block, acceptance criteria,
  problem statement, implementation plan, etc.

### 2. Crash/Restart Recovery
- Added `resetStuckFeatures()` to clean up transient states on auto-mode start
- Features stuck in `in_progress` are reset to `ready` or `backlog`
- Tasks stuck in `in_progress` are reset to `pending`
- Plan generation stuck in `generating` is reset to `pending`
- `loadPendingFeatures()` now includes recovery cases for interrupted executions
- Persisted task status in `planSpec.tasks` array allows resuming from last completed task

### 3. Spec Todo List UI Updates
- Added `ParsedTask` and `PlanSpec` types to `@automaker/types` for consistent typing
- New `auto_mode_task_status` event emitted when task status changes
- New `auto_mode_summary` event emitted when summary is extracted
- Query invalidation triggers on task status updates for real-time UI refresh
- Task markers (`[TASK_START]`, `[TASK_COMPLETE]`, `[PHASE_COMPLETE]`) are detected
  and persisted to planSpec.tasks for UI display

### 4. Summary Extraction
- Added `extractSummary()` function to parse summaries from multiple formats:
  - `<summary>` tags (explicit)
  - `## Summary` sections (markdown)
  - `**Goal**:` sections (lite mode)
  - `**Problem**:` sections (spec/full modes)
  - `**Solution**:` sections (fallback)
- Summary is saved to `feature.summary` field after execution
- Summary is extracted from plan content during spec generation

### 5. Worktree Mode Support (#619)
- Recovery logic properly handles branchName filtering
- Features in worktrees maintain correct association during recovery

## Files Changed
- libs/types/src/feature.ts - Added ParsedTask and PlanSpec interfaces
- libs/types/src/index.ts - Export new types
- apps/server/src/services/auto-mode-service.ts - Core fixes for all issues
- apps/server/tests/unit/services/auto-mode-task-parsing.test.ts - New tests
- apps/ui/src/store/app-store.ts - Import types from @automaker/types
- apps/ui/src/hooks/use-auto-mode.ts - Handle new events
- apps/ui/src/hooks/use-query-invalidation.ts - Invalidate on task updates
- apps/ui/src/types/electron.d.ts - New event type definitions
- apps/ui/src/components/views/board-view/dialogs/*.tsx - Enable planning for all models

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

apps/ui/src/store/app-store.ts

@@ -37,6 +37,8 @@ import type {
   ClaudeApiProfile,
   ClaudeCompatibleProvider,
   SidebarStyle,
+  ParsedTask,
+  PlanSpec,
 } from '@automaker/types';
 import {
   getAllCursorModelIds,
@@ -65,6 +67,8 @@ export type {
   ServerLogLevel,
   FeatureTextFilePath,
   FeatureImagePath,
+  ParsedTask,
+  PlanSpec,
 };
 
 export type ViewMode =
@@ -469,28 +473,7 @@ export interface Feature extends Omit<
   planSpec?: PlanSpec; // Explicit planSpec type to override BaseFeature's index signature
 }
 
-// Parsed task from spec (for spec and full planning modes)
-export interface ParsedTask {
-  id: string; // e.g., "T001"
-  description: string; // e.g., "Create user model"
-  filePath?: string; // e.g., "src/models/user.ts"
-  phase?: string; // e.g., "Phase 1: Foundation" (for full mode)
-  status: 'pending' | 'in_progress' | 'completed' | 'failed';
-}
-
-// PlanSpec status for feature planning/specification
-export interface PlanSpec {
-  status: 'pending' | 'generating' | 'generated' | 'approved' | 'rejected';
-  content?: string; // The actual spec/plan markdown content
-  version: number;
-  generatedAt?: string; // ISO timestamp
-  approvedAt?: string; // ISO timestamp
-  reviewedByUser: boolean; // True if user has seen the spec
-  tasksCompleted?: number;
-  tasksTotal?: number;
-  currentTaskId?: string; // ID of the task currently being worked on
-  tasks?: ParsedTask[]; // Parsed tasks from the spec
-}
+// ParsedTask and PlanSpec types are now imported from @automaker/types
 
 // File tree node for project analysis
 export interface FileTreeNode {