fix: persist TUI branch sessions

[HamsteRider-m]

What

• Persist TUI2 /branch snapshots into temp/model_responses using the existing /continue raw log format.
• Register the branch name with session_names so named branches are discoverable.
• Point the branched agent and its LLM clients at the new snapshot log so future turns append to the branched session instead of the source session.

Why

Before this change, /branch only copied in-memory UI/backend state. If the branched session was later searched via /continue, there was no standalone log for that branch, and branch names could resolve to the wrong/current session log.

Testing

• python -m py_compile frontends/tuiapp_v2.py
• Targeted restore check: _persist_branch_snapshot() output is parsed by continue_cmd._pairs() + _parse_native_history() and matches the expected restored history.
• git diff --check --cached -- frontends/tuiapp_v2.py

Note: local commit used --no-verify because this checkout's pre-commit hook points to a missing scripts/plantree_pre_commit.py; the checks above were run manually before committing.