/clear should expose new conversation ID (e.g. via hook or env var)

Problem

When using Claude Code inside tmux with a custom session-resume workflow, /clear starts a new conversation internally — but the new conversation ID is not exposed anywhere. This makes it impossible to update external session tracking after a clear.

Context: tmux session resume pattern

A common pattern for persistent Claude Code sessions in tmux looks like this:

1. On first launch, generate a UUID and start Claude with --session-id <uuid>, save it to a file (e.g. .claude-session-id)
2. On reattach, if the tmux session already exists — just attach
3. If the tmux session is gone (reboot, crash) — read the saved ID and resume with claude --resume <id>

This gives you persistent, resumable Claude sessions across terminal reconnects.

if [[ ! -f "$SESSION_ID_FILE" ]]; then
    uuidgen > "$SESSION_ID_FILE"
    CLAUDE_CMD="claude --session-id '$(cat "$SESSION_ID_FILE")'"
else
    CLAUDE_CMD="claude --resume '$(cat "$SESSION_ID_FILE")'"
fi

The gap: /clear breaks the chain

When the user runs /clear inside Claude Code:

• A new conversation is started internally
• But the new conversation ID is not exposed anywhere (no env var, no hook event)
• .claude-session-id still contains the old ID
• Next time the tmux session is gone and the user reconnects, claude --resume <old-id> restores the pre-clear conversation

Why a hook workaround doesn't work

A UserPromptSubmit hook on /clear can detect the command, but:

• It can delete the file — so next launch gets a fresh session (acceptable)
• It cannot write the new ID — because the new conversation ID isn't available at hook time

Suggested fix

Either:

• Add a ConversationClear hook event that exposes the new conversation ID (e.g. as $CLAUDE_SESSION_ID env var), or
• Write the new conversation ID to a known location after /clear so external tooling can read it

This would allow users to keep their session tracking files in sync with Claude Code's internal state.