[FEATURE] Show project name/git info instead of '원격 제어' in Claude app remote control sessions

Description

When using Claude Code CLI connected to the Claude app (mobile/desktop), some sessions show the project name as the subtitle under the session title, while others only show "원격 제어" (Remote Control).

Previously, git information / project context was displayed in the subtitle area, but now it often just says "원격 제어".

Expected Behavior

The Claude app should consistently show the project name (or git branch info) as the session subtitle, even when the session is connected via Remote Control mode — similar to how it already works in some sessions.

Screenshots

Working (shows project name):

• Session subtitle displays the project directory name

Current issue (shows only "원격 제어"):

• Session subtitle displays "원격 제어" instead of the project name

Environment

• Claude Code CLI (latest)
• Claude app (iOS)
• macOS

Additional Context

The statusline is properly configured in settings.json with a custom script that outputs git branch, staged/modified counts, model name, and context usage. The issue seems to be in the Claude app UI layer, not the CLI configuration.