feat(ui): display branch name in terminal header with git icon

- Move branch name display from tab name to terminal header
- Show full branch name (no truncation) with GitBranch icon
- Display branch name for both 'new tab' and 'split' modes
- Persist openTerminalMode setting to server and include in import/export
- Update settings dropdown to simplified "New Tab" label

apps/ui/src/lib/http-api-client.ts

@@ -1805,8 +1805,6 @@ export class HttpApiClient implements ElectronAPI {
       this.post('/api/worktree/switch-branch', { worktreePath, branchName }),
     openInEditor: (worktreePath: string, editorCommand?: string) =>
       this.post('/api/worktree/open-in-editor', { worktreePath, editorCommand }),
-    openInTerminal: (worktreePath: string) =>
-      this.post('/api/worktree/open-in-terminal', { worktreePath }),
     getDefaultEditor: () => this.get('/api/worktree/default-editor'),
     getAvailableEditors: () => this.get('/api/worktree/available-editors'),
     refreshEditors: () => this.post('/api/worktree/refresh-editors', {}),