[Feature]: Expose current thread info via environment variables #3003

Before submitting

• I searched existing issues and did not find a duplicate.
• I am describing a concrete problem or use case, not just a vague idea.

Area

apps/server

Problem or use case

I want to have information about current thread in environment variables: both for terminal and running agent sessions.

Proposed solution

Provide environment variables along project and thread scoped child processes (terminal and harness):

1. T3CODE_PROJECT_ROOT (currently available only in terminal - make available everywhere)
2. T3CODE_WORKTREE_PATH (currently available only in terminal, if worktree is used - make available everywhere)
3. T3CODE_PROJECT_ID (add new)
4. T3CODE_THREAD_ID (add new)
5. T3CODE_HOME - always provide resolved path - canonical value

Cool ideas for future, but out of scope:

1. T3CODE_ORIGIN - accessible server host
2. T3CODE_TOKEN - short living scoped token that allows controlling only threads in current project or something like this

Why this matters

Cool automation opportunities - like using custom CLI (see references) that allows agent to create threads in t3code, control them.

Smallest useful scope

Adding those two:

1. T3CODE_PROJECT_ID
2. T3CODE_THREAD_ID

Alternatives considered

Using cwd as context, but can't detect thread reliable this way.

Risks or tradeoffs

Claude relying on T3* env variables presence to detect it's running under t3code?

Examples or references

Currently t3code provides two environment variables in terminal: T3CODE_PROJECT_ROOT, T3CODE_WORKTREE_PATH.

#2921
https://github.com/kcosr/t3code-threads
https://github.com/tarik02/t3code-cli

Contribution

• I would be open to helping implement this.