Add per-turn prompt cache TTL options (#59480)

## What changed

- Expose `PromptCacheTtl` through `TurnStartOptions` and `RecoverTurnRequest`, supporting `30m` and `12h` minimum cache lifetimes.
- Carry the selected TTL through turn execution and compaction into `prompt_cache_options.ttl` on Responses HTTP and WebSocket requests. Omit the field when unset and keep the selection scoped to the turn.
- Include prompt cache options in WebSocket request reuse checks.

## Testing

Add coverage for both TTL values and omission on a subsequent turn without an override, and extend WebSocket serialization coverage to include prompt cache options.

GitOrigin-RevId: 8529306e6ad6030fe77c5e6bf19f3810717c0c5e

codex-rs/codex-api/src/common.rs

@@ -10,6 +10,7 @@ use codex_protocol::protocol::TokenUsage;
 use codex_protocol::protocol::TurnModerationMetadataEvent;
 use codex_protocol::protocol::W3cTraceContext;
 use codex_protocol::turn_input::CyberAccessProgram;
+use codex_protocol::turn_input::PromptCacheTtl;
 use futures::Stream;
 use serde::Deserialize;
 use serde::Serialize;
@@ -277,6 +278,11 @@ impl Serialize for ResponsesApiTools {
     }
 }
 
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize)]
+pub struct PromptCacheOptions {
+    pub ttl: PromptCacheTtl,
+}
+
 #[derive(Debug, Serialize, Clone, PartialEq)]
 pub struct ResponsesApiRequest {
     // Keep routing fields first: serde serializes struct fields in declaration order, and
@@ -298,6 +304,8 @@ pub struct ResponsesApiRequest {
     #[serde(skip_serializing_if = "Option::is_none")]
     pub prompt_cache_key: Option<String>,
     #[serde(skip_serializing_if = "Option::is_none")]
+    pub prompt_cache_options: Option<PromptCacheOptions>,
+    #[serde(skip_serializing_if = "Option::is_none")]
     pub text: Option<TextControls>,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub client_metadata: Option<HashMap<String, String>>,
@@ -321,6 +329,7 @@ impl<'a> From<&'a ResponsesApiRequest> for ResponseCreateWsRequest<'a> {
             include: &request.include,
             service_tier: request.service_tier.as_deref(),
             prompt_cache_key: request.prompt_cache_key.as_deref(),
+            prompt_cache_options: request.prompt_cache_options,
             text: request.text.as_ref(),
             generate: None,
             client_metadata: request.client_metadata.clone(),
@@ -352,6 +361,8 @@ pub struct ResponseCreateWsRequest<'a> {
     #[serde(skip_serializing_if = "Option::is_none")]
     pub prompt_cache_key: Option<&'a str>,
     #[serde(skip_serializing_if = "Option::is_none")]
+    pub prompt_cache_options: Option<PromptCacheOptions>,
+    #[serde(skip_serializing_if = "Option::is_none")]
     pub text: Option<&'a TextControls>,
     #[serde(skip_serializing_if = "Option::is_none")]
     pub generate: Option<bool>,

codex-rs/codex-api/src/endpoint/responses_websocket.rs

@@ -1117,6 +1117,9 @@ mod tests {
             include: vec!["reasoning.encrypted_content".to_string()],
             service_tier: Some("priority".to_string()),
             prompt_cache_key: Some("cache-key".to_string()),
+            prompt_cache_options: Some(crate::PromptCacheOptions {
+                ttl: codex_protocol::turn_input::PromptCacheTtl::TwelveHours,
+            }),
             text: None,
             access_programs: Some(
                 codex_protocol::turn_input::CyberAccessProgram::DaybreakBlue.into(),

codex-rs/codex-api/src/lib.rs

@@ -37,6 +37,7 @@ pub use crate::common::AccessPrograms;
 pub use crate::common::MemorySummarizeInput;
 pub use crate::common::MemorySummarizeOutput;
 pub use crate::common::OpenAiVerbosity;
+pub use crate::common::PromptCacheOptions;
 pub use crate::common::RawMemory;
 pub use crate::common::RawMemoryMetadata;
 pub use crate::common::Reasoning;