fix: always send full instructions when using the Responses API (#1207)

This fixes a longstanding error in the Rust CLI where `codex.rs`
contained an errant `is_first_turn` check that would exclude the user
instructions for subsequent "turns" of a conversation when using the
responses API (i.e., when `previous_response_id` existed).

While here, renames `Prompt.instructions` to `Prompt.user_instructions`
since we now have quite a few levels of instructions floating around.
Also removed an unnecessary use of `clone()` in
`Prompt.get_full_instructions()`.

codex-rs/core/src/client_common.rs

@@ -25,7 +25,7 @@ pub struct Prompt {
     pub prev_id: Option<String>,
     /// Optional instructions from the user to amend to the built-in agent
     /// instructions.
-    pub instructions: Option<String>,
+    pub user_instructions: Option<String>,
     /// Whether to store response on server side (disable_response_storage = !store).
     pub store: bool,
 
@@ -37,21 +37,14 @@ pub struct Prompt {
 
 impl Prompt {
     pub(crate) fn get_full_instructions(&self, model: &str) -> Cow<str> {
-        [
-            Some(Cow::Borrowed(BASE_INSTRUCTIONS)),
-            self.instructions.as_ref().map(|s| Cow::Owned(s.clone())),
-            if model.starts_with("gpt-4.1") {
-                Some(Cow::Borrowed(APPLY_PATCH_TOOL_INSTRUCTIONS))
-            } else {
-                None
-            },
-        ]
-        .iter()
-        .filter_map(|s| s.as_ref())
-        .map(|cow| cow.as_ref())
-        .collect::<Vec<_>>()
-        .join("\n")
-        .into()
+        let mut sections: Vec<&str> = vec![BASE_INSTRUCTIONS];
+        if let Some(ref user) = self.user_instructions {
+            sections.push(user);
+        }
+        if model.starts_with("gpt-4.1") {
+            sections.push(APPLY_PATCH_TOOL_INSTRUCTIONS);
+        }
+        Cow::Owned(sections.join("\n"))
     }
 }