feat: add git worktree session support with improved UI

Implement comprehensive worktree session support allowing users to spawn sessions in temporary git worktrees. Includes backend worktree management, full-stack integration, and refined UI for session type selection.

Backend:
- Add worktree creation/removal utilities with branch management
- Track worktree metadata (basePath, branch, name, path) in session metadata
- Automatic cleanup of worktrees when sessions fail or exit
- Enhanced error handling with stderr tail logging

UI improvements:
- Redesign session type toggle with improved alignment and spacing
- Move worktree description inline with label for cleaner layout
- Add branch name input field that appears when worktree mode selected
- Auto-focus on worktree input when switching modes
- Reduce gap between radio options from gap-3 to gap-1.5
- Update descriptive text and placeholders for clarity

Integration:
- Thread worktree parameters through API client, RPC handlers, and daemon
- Add worktreeEnv utility to read worktree info from environment
- Update session spawning to support both simple and worktree modes

server/src/sync/syncEngine.ts

@@ -28,7 +28,14 @@ export const MetadataSchema = z.object({
     }).optional(),
     machineId: z.string().optional(),
     tools: z.array(z.string()).optional(),
-    flavor: z.string().nullish()
+    flavor: z.string().nullish(),
+    worktree: z.object({
+        basePath: z.string(),
+        branch: z.string(),
+        name: z.string(),
+        worktreePath: z.string().optional(),
+        createdAt: z.number().optional()
+    }).optional()
 }).passthrough()
 
 export type Metadata = z.infer<typeof MetadataSchema>
@@ -653,13 +660,15 @@ export class SyncEngine {
         machineId: string,
         directory: string,
         agent: 'claude' | 'codex' | 'gemini' = 'claude',
-        yolo?: boolean
+        yolo?: boolean,
+        sessionType?: 'simple' | 'worktree',
+        worktreeName?: string
     ): Promise<{ type: 'success'; sessionId: string } | { type: 'error'; message: string }> {
         try {
             const result = await this.machineRpc(
                 machineId,
                 'spawn-happy-session',
-                { type: 'spawn-in-directory', directory, agent, yolo }
+                { type: 'spawn-in-directory', directory, agent, yolo, sessionType, worktreeName }
             )
             if (result && typeof result === 'object') {
                 const obj = result as Record<string, unknown>

server/src/web/routes/machines.ts

@@ -6,7 +6,9 @@ import type { WebAppEnv } from '../middleware/auth'
 const spawnBodySchema = z.object({
     directory: z.string().min(1),
     agent: z.enum(['claude', 'codex', 'gemini']).optional(),
-    yolo: z.boolean().optional()
+    yolo: z.boolean().optional(),
+    sessionType: z.enum(['simple', 'worktree']).optional(),
+    worktreeName: z.string().optional()
 })
 
 export function createMachinesRoutes(getSyncEngine: () => SyncEngine | null): Hono<WebAppEnv> {
@@ -44,7 +46,9 @@ export function createMachinesRoutes(getSyncEngine: () => SyncEngine | null): Ho
             machineId,
             parsed.data.directory,
             parsed.data.agent,
-            parsed.data.yolo
+            parsed.data.yolo,
+            parsed.data.sessionType,
+            parsed.data.worktreeName
         )
         return c.json(result)
     })

server/src/web/routes/sessions.ts

@@ -9,6 +9,13 @@ type SessionSummaryMetadata = {
     path: string
     summary?: { text: string }
     flavor?: string | null
+    worktree?: {
+        basePath: string
+        branch: string
+        name: string
+        worktreePath?: string
+        createdAt?: number
+    }
 }
 
 type SessionSummary = {
@@ -29,7 +36,8 @@ function toSessionSummary(session: Session): SessionSummary {
         name: session.metadata.name,
         path: session.metadata.path,
         summary: session.metadata.summary ? { text: session.metadata.summary.text } : undefined,
-        flavor: session.metadata.flavor ?? null
+        flavor: session.metadata.flavor ?? null,
+        worktree: session.metadata.worktree
     } : null
 
     const todoProgress = session.todos?.length ? {