[app-server] remove serde(skip_serializing_if = "Option::is_none") annotations (#5939)

We had this annotation everywhere in app-server APIs which made it so
that fields get serialized as `field?: T`, meaning if the field as
`None` we would omit the field in the payload. Removing this annotation
changes it so that we return `field: T | null` instead, which makes
codex app-server's API more aligned with the convention of public OpenAI
APIs like Responses.

Separately, remove the `#[ts(optional_fields = nullable)]` annotations
that were recently added which made all the TS types become `field?: T |
null` which is not great since clients need to handle undefined and
null.

I think generally it'll be best to have optional types be either:
- `field: T | null` (preferred, aligned with public OpenAI APIs)
- `field?: T` where we have to, such as types generated from the MCP
schema:
https://github.com/modelcontextprotocol/modelcontextprotocol/blob/main/schema/2025-06-18/schema.ts
(see changes to `mcp-types/`)

I updated @etraut-openai's unit test to check that all generated TS
types are one or the other, not both (so will error if we have a type
that has `field?: T | null`). I don't think there's currently a good use
case for that - but we can always revisit.

codex-rs/protocol/src/models.rs

@@ -48,36 +48,35 @@ pub enum ContentItem {
 #[serde(tag = "type", rename_all = "snake_case")]
 pub enum ResponseItem {
     Message {
-        #[serde(skip_serializing)]
-        #[ts(optional = nullable)]
+        #[serde(default, skip_serializing)]
+        #[ts(skip)]
         id: Option<String>,
         role: String,
         content: Vec<ContentItem>,
     },
     Reasoning {
         #[serde(default, skip_serializing)]
+        #[ts(skip)]
         id: String,
         summary: Vec<ReasoningItemReasoningSummary>,
         #[serde(default, skip_serializing_if = "should_serialize_reasoning_content")]
-        #[ts(optional = nullable)]
+        #[ts(optional)]
         content: Option<Vec<ReasoningItemContent>>,
-        #[ts(optional = nullable)]
         encrypted_content: Option<String>,
     },
     LocalShellCall {
         /// Set when using the chat completions API.
-        #[serde(skip_serializing)]
-        #[ts(optional = nullable)]
+        #[serde(default, skip_serializing)]
+        #[ts(skip)]
         id: Option<String>,
         /// Set when using the Responses API.
-        #[ts(optional = nullable)]
         call_id: Option<String>,
         status: LocalShellStatus,
         action: LocalShellAction,
     },
     FunctionCall {
-        #[serde(skip_serializing)]
-        #[ts(optional = nullable)]
+        #[serde(default, skip_serializing)]
+        #[ts(skip)]
         id: Option<String>,
         name: String,
         // The Responses API returns the function call arguments as a *string* that contains
@@ -97,11 +96,11 @@ pub enum ResponseItem {
         output: FunctionCallOutputPayload,
     },
     CustomToolCall {
-        #[serde(skip_serializing)]
-        #[ts(optional = nullable)]
+        #[serde(default, skip_serializing)]
+        #[ts(skip)]
         id: Option<String>,
         #[serde(default, skip_serializing_if = "Option::is_none")]
-        #[ts(optional = nullable)]
+        #[ts(optional)]
         status: Option<String>,
 
         call_id: String,
@@ -121,11 +120,11 @@ pub enum ResponseItem {
     //   "action": {"type":"search","query":"weather: San Francisco, CA"}
     // }
     WebSearchCall {
-        #[serde(skip_serializing)]
-        #[ts(optional = nullable)]
+        #[serde(default, skip_serializing)]
+        #[ts(skip)]
         id: Option<String>,
         #[serde(default, skip_serializing_if = "Option::is_none")]
-        #[ts(optional = nullable)]
+        #[ts(optional)]
         status: Option<String>,
         action: WebSearchAction,
     },
@@ -203,7 +202,6 @@ pub enum LocalShellAction {
 }
 
 #[derive(Debug, Clone, Serialize, Deserialize, PartialEq, JsonSchema, TS)]
-#[ts(optional_fields = nullable)]
 pub struct LocalShellExecAction {
     pub command: Vec<String>,
     pub timeout_ms: Option<u64>,
@@ -296,7 +294,6 @@ impl From<Vec<UserInput>> for ResponseInputItem {
 /// If the `name` of a `ResponseItem::FunctionCall` is either `container.exec`
 /// or shell`, the `arguments` field should deserialize to this struct.
 #[derive(Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
-#[ts(optional_fields = nullable)]
 pub struct ShellToolCallParams {
     pub command: Vec<String>,
     pub workdir: Option<String>,
@@ -329,7 +326,6 @@ pub enum FunctionCallOutputContentItem {
 /// `content_items` with the structured form that the Responses/Chat
 /// Completions APIs understand.
 #[derive(Debug, Default, Clone, PartialEq, JsonSchema, TS)]
-#[ts(optional_fields = nullable)]
 pub struct FunctionCallOutputPayload {
     pub content: String,
     #[serde(skip_serializing_if = "Option::is_none")]