fix(core) Preserve base_instructions in SessionMeta (#9427)

## Summary
This PR consolidates base_instructions onto SessionMeta /
SessionConfiguration, so we ensure `base_instructions` is set once per
session and should be (mostly) immutable, unless:
- overridden by config on resume / fork
- sub-agent tasks, like review or collab


In a future PR, we should convert all references to `base_instructions`
to consistently used the typed struct, so it's less likely that we put
other strings there. See #9423. However, this PR is already quite
complex, so I'm deferring that to a follow-up.

## Testing
- [x] Added a resume test to assert that instructions are preserved. In
particular, `resume_switches_models_preserves_base_instructions` fails
against main.

Existing test coverage thats assert base instructions are preserved
across multiple requests in a session:
- Manual compact keeps baseline instructions:
core/tests/suite/compact.rs:199
- Auto-compact keeps baseline instructions:
core/tests/suite/compact.rs:1142
- Prompt caching reuses the same instructions across two requests:
core/tests/suite/prompt_caching.rs:150 and
core/tests/suite/prompt_caching.rs:157
- Prompt caching with explicit expected string across two requests:
core/tests/suite/prompt_caching.rs:213 and
core/tests/suite/prompt_caching.rs:222
- Resume with model switch keeps original instructions:
core/tests/suite/resume.rs:136
- Compact/resume/fork uses request 0 instructions for later expected
payloads: core/tests/suite/compact_resume_fork.rs:215

codex-rs/protocol/src/models.rs

@@ -167,6 +167,23 @@ pub enum ResponseItem {
     Other,
 }
 
+pub const BASE_INSTRUCTIONS_DEFAULT: &str = include_str!("prompts/base_instructions/default.md");
+
+/// Base instructions for the model in a thread. Corresponds to the `instructions` field in the ResponsesAPI.
+#[derive(Debug, Clone, Serialize, Deserialize, PartialEq, JsonSchema, TS)]
+#[serde(rename = "base_instructions", rename_all = "snake_case")]
+pub struct BaseInstructions {
+    pub text: String,
+}
+
+impl Default for BaseInstructions {
+    fn default() -> Self {
+        Self {
+            text: BASE_INSTRUCTIONS_DEFAULT.to_string(),
+        }
+    }
+}
+
 /// Developer-provided guidance that is injected into a turn as a developer role
 /// message.
 #[derive(Debug, Clone, Serialize, Deserialize, PartialEq, JsonSchema, TS)]