Strip CLAUDECODE from the Claude Code subprocess env

[jhampton]

Problem

The Claude Code CLI refuses to start when the CLAUDECODE environment variable is set, treating it as an attempt to nest a session inside another Claude Code session. When the host process that calls buildClaudeSubprocessEnv() is itself launched from inside a Claude Code session, it inherits CLAUDECODE from its own environment. That value is then spread into the spawned CLI's env, so the subprocess sees CLAUDECODE set, interprets it as a nested-session attempt, and never comes up — the SDK transport gets no valid handshake.

This affects anyone running the app from inside a Claude Code session (a common development and automation setup).

Fix

Delete CLAUDECODE from the subprocess environment in buildClaudeSubprocessEnv(), right after the base environment is assembled and before it is handed to the SDK. The host's own session context no longer leaks into spawned CLIs; standalone spawns are unaffected.

The change is one line plus an explanatory comment, adjacent to the existing Bedrock-routing strips in the same function.

Test plan

Adds packages/shared/tests/claude-subprocess-env.test.ts:

• strips CLAUDECODE from the subprocess env — sets process.env.CLAUDECODE and asserts the built env omits it.
• strips Claude-specific Bedrock routing vars — regression guard for the existing Bedrock strips (previously untested).
• preserves unrelated environment variables — confirms the strip is surgical and envOverrides pass through.

Validation:

• bun test tests/claude-subprocess-env.test.ts in packages/shared → 3 pass, 0 fail.
• tsc --noEmit on packages/shared → 0 errors.