Document a stable way for agents and hooks to detect a T3 Code session

[Slava-code]

Problem

Many people keep global agent instructions (~/.claude/CLAUDE.md, ~/.codex/AGENTS.md) that apply to every session: terminal, IDE, and T3 Code. Some guidance only makes sense inside T3. For example:

• use the preview_* tools for localhost;
• in a Claude thread, hand computer use to a Codex child with delegate_task, because Claude Code's own computer use isn't available in Agent SDK sessions.

There's no documented signal an agent, hook, or script can check to know it's running under T3 Code, so these instructions have to rely on something unofficial.

What works today, and why it's fragile

• The t3-code MCP tools appear in the tool list. The model can see that, but scripts and hooks can't.
• T3CODE_THREAD_ID is set in Claude sessions, Codex shells and ACP sessions. But it exists for preview port discovery (PortScanner.AGENT_THREAD_ENV) and isn't in the user docs, so it could be renamed or scoped down at any time.

Proposal

Document one stable signal, either:

• mark T3CODE_THREAD_ID as supported in the user docs, or
• add a simple marker next to it in every provider's environment, such as T3CODE=1.

A one-line note on detecting a T3 Code session from instructions or hooks would be enough. I'm happy to send the docs change if the direction is OK.