Put Default-mode request_user_input back in /experimental

[charley-oai]

Summary

• move DefaultModeRequestUserInput back to Stage::Experimental
• keep it default-off and add /experimental menu metadata so users can opt in explicitly
• preserve the canonical feature key default_mode_request_user_input and the normal features.default_mode_request_user_input override path
• update core tests to restore default-off behavior while keeping explicit opt-in coverage for Default mode

Statsig compatibility

• this PR does not add Statsig gate wiring in codex-rs
• it keeps the feature compatible with the existing app/desktop Statsig override flow because overrides already materialize as features.<key> config entries on thread/start
• when ready, codex-apps can wire a Statsig gate or layer to default_mode_request_user_input through the existing statsig_default_enable_features / feature-overrides plumbing

Testing

• just fmt
• cargo test -p codex-core
  • locally red in this environment for unrelated existing issues:
    • missing test_stdio_server helper binary breaks several rmcp_client / plugin / truncation tests
    • unrelated search_tool::* tests also failed locally
• cargo test -p codex-core features::tests::default_mode_request_user_input_is_experimental_and_user_toggleable -- --exact
• cargo test -p codex-core tools::spec::tests::request_user_input_description_reflects_default_mode_feature_flag -- --exact
• cargo test -p codex-app-server experimental_feature_list -- --nocapture

[charley-oai]

@codex review this

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Another round soon, please!

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