Authenticate Code Everywhere HTTP client

[cbusillo]

Summary

• attach remote_inbox.token bearer auth to Code Everywhere HTTP events, snapshot checks, and command claims
• add focused regression coverage for trimming and omitting empty auth tokens

Validation

• cargo test -p code-tui code_everywhere_http_auth_header_uses_remote_inbox_token --features test-helpers
• cargo test -p code-tui remote_inbox --features test-helpers
• cargo build -p code-cli --features code-tui/test-helpers
• ./build-fast.sh
• CODE_EVERYWHERE_CODE_BINARY=/Users/cbusillo/.code/working/code/branches/http-auth-token-clean-1777553873/code-rs/target/debug/code pnpm smoke:cockpit:real-tui
• CODE_EVERYWHERE_CODE_BINARY=/Users/cbusillo/.code/working/code/branches/http-auth-token-clean-1777553873/code-rs/target/debug/code pnpm smoke:cockpit:real-tui:pending-work

Notes

This isolates the Apple proof blocker from the unrelated dirty ../code worktree. The branch changes only code-rs/tui/src/remote_inbox/client.rs.