Move default realtime prompt into core (#17165)

- Adds a core-owned realtime backend prompt template and preparation
path.
- Makes omitted realtime start prompts use the core default, while null
or empty prompts intentionally send empty instructions.
- Covers the core realtime path and app-server v2 path with integration
coverage.

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/core/src/lib.rs

@@ -13,6 +13,7 @@ mod client_common;
 pub(crate) mod codex;
 mod realtime_context;
 mod realtime_conversation;
+mod realtime_prompt;
 pub use codex::SteerInputError;
 mod codex_thread;
 mod compact_remote;