Never store requests (#3212)

When item ids are sent to Responses API it will load them from the
database ignoring the provided values. This adds extra latency.

Not having the mode to store requests also allows us to simplify the
code.

## Breaking change

The `disable_response_storage` configuration option is removed.

codex-rs/mcp-server/src/codex_message_processor.rs

@@ -994,7 +994,6 @@ fn derive_config_from_params(
         include_plan_tool,
         include_apply_patch_tool,
         include_view_image_tool: None,
-        disable_response_storage: None,
         show_raw_agent_reasoning: None,
         tools_web_search_request: None,
     };

codex-rs/mcp-server/src/codex_tool_config.rs

@@ -162,7 +162,6 @@ impl CodexToolCallParam {
             include_plan_tool,
             include_apply_patch_tool: None,
             include_view_image_tool: None,
-            disable_response_storage: None,
             show_raw_agent_reasoning: None,
             tools_web_search_request: None,
         };

codex-rs/mcp-server/tests/suite/config.rs

@@ -51,7 +51,6 @@ model_reasoning_effort = "high"
 model_reasoning_summary = "detailed"
 model_verbosity = "medium"
 model_provider = "openai"
-disable_response_storage = false
 chatgpt_base_url = "https://api.chatgpt.com"
 "#,
     )
@@ -111,7 +110,6 @@ async fn get_config_toml_parses_all_fields() {
                     model_reasoning_summary: Some(ReasoningSummary::Detailed),
                     model_verbosity: Some(Verbosity::Medium),
                     model_provider: Some("openai".into()),
-                    disable_response_storage: Some(false),
                     chatgpt_base_url: Some("https://api.chatgpt.com".into()),
                 },
             )]),