feat(claude): add 'auto' startup permission mode

Adds Anthropic's classifier-guarded low-prompt mode (--permission-mode
auto) as a fourth ClaudeMode alongside skip-permissions/normal/allowedTools.
Wired through both spawn paths (buildPermissionArgs for direct PTY,
buildClaudePermissionFlags for tmux), the getClaudeModeConfig validator,
and the App Settings Startup Mode picker. Exports buildSpawnCommand for
test coverage.

This is the prerequisite for multi-user mode section 6.3, which downgrades
non-granted users' sessions to 'auto'.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

src/web/public/index.html

@@ -1449,6 +1449,7 @@
               <label>Startup Mode</label>
               <select id="appSettingsClaudeMode" class="form-select">
                 <option value="dangerously-skip-permissions">Skip Permissions (default)</option>
+                <option value="auto">Auto (classifier-guarded, low prompts)</option>
                 <option value="normal">Normal (with prompts)</option>
                 <option value="allowedTools">Allowed Tools Only</option>
               </select>

src/web/server.ts

@@ -1514,7 +1514,12 @@ export class WebServer extends EventEmitter {
     const claudeMode = settings.claudeMode as string | undefined;
     const allowedTools = settings.allowedTools as string | undefined;
     // Only return valid modes
-    if (claudeMode === 'dangerously-skip-permissions' || claudeMode === 'normal' || claudeMode === 'allowedTools') {
+    if (
+      claudeMode === 'dangerously-skip-permissions' ||
+      claudeMode === 'auto' ||
+      claudeMode === 'normal' ||
+      claudeMode === 'allowedTools'
+    ) {
       return { claudeMode, allowedTools };
     }
     return {};