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

cli/src/claude/runClaude.ts

@@ -24,6 +24,7 @@ import { registerKillSessionHandler } from './registerKillSessionHandler';
 import { runtimePath } from '../projectPath';
 import { resolve } from 'node:path';
 import type { Session } from './session';
+import { readWorktreeEnv } from '@/utils/worktreeEnv';
 
 export interface StartOptions {
     model?: string
@@ -73,6 +74,7 @@ export async function runClaude(options: StartOptions = {}): Promise<void> {
         metadata: initialMachineMetadata
     });
 
+    const worktreeInfo = readWorktreeEnv();
     let metadata: Metadata = {
         path: workingDirectory,
         host: os.hostname(),
@@ -89,7 +91,8 @@ export async function runClaude(options: StartOptions = {}): Promise<void> {
         // Initialize lifecycle state
         lifecycleState: 'running',
         lifecycleStateSince: Date.now(),
-        flavor: 'claude'
+        flavor: 'claude',
+        worktree: worktreeInfo ?? undefined
     };
     const response = await api.getOrCreateSession({ tag: sessionTag, metadata, state });
     logger.debug(`Session created: ${response.id}`);