chore: remove dead tests and docs for removed TUI auto-open feature

[JeremyDev87]

Parent

• refactor(tui): remove TUI auto-open and adopt single TUI multi-session model #1111

Summary

Wave 1 (#1112, #1113) removed the TUI auto-open/close code but left behind dead tests and stale documentation that reference the deleted functions. This issue cleans them up.

Dead Tests

1. Delete packages/claude-code-plugin/tests/test_tmux_sidebar.py (entire file)

Tests for _setup_tmux_sidebar(), _sidebar_pane_exists(), TMUX_SUGGESTION — all removed in #1112.

2. Delete TestTuiSidebarCleanup class from packages/claude-code-plugin/tests/test_stop.py

Tests for _close_tui_sidebar() — removed in #1112.

3. Delete test_sets_auto_tui_to_zero from packages/claude-code-plugin/tests/test_session_start_hud.py

Tests for CODINGBUDDY_AUTO_TUI=0 setting logic — removed in #1112.

Stale Documentation

4. Remove auto-launch sections from docs/tui-troubleshooting.md

• "Auto-Launch Issues" section (~lines 506-535)
• "Auto-Launch Environment Variable Reference" table (~lines 587-591)

5. Mirror changes in docs/ko/tui-troubleshooting.md

Korean translation of the same auto-launch sections.

6. Delete docs/plans/2026-03-28-wave3-auto-install-tmux-sidebar.md

Obsolete implementation plan for the removed feature.

Verification

# Dead test references gone
grep -rn "_setup_tmux_sidebar\|_close_tui_sidebar\|test_sets_auto_tui_to_zero" packages/claude-code-plugin/tests/

# Python tests still pass
cd packages/claude-code-plugin && python3 -m pytest tests/ -x --tb=short

# No broken imports
python3 -c "
import ast
for f in ['tests/test_stop.py', 'tests/test_session_start_hud.py']:
    ast.parse(open(f'packages/claude-code-plugin/{f}').read())
print('Syntax OK')
"

Acceptance Criteria

• test_tmux_sidebar.py deleted
• TestTuiSidebarCleanup class removed from test_stop.py
• test_sets_auto_tui_to_zero removed from test_session_start_hud.py
• Auto-launch sections removed from docs/tui-troubleshooting.md
• Auto-launch sections removed from docs/ko/tui-troubleshooting.md
• Obsolete plan doc deleted
• Remaining tests pass