[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/app-server-protocol/src/jsonrpc_lite.rs

@@ -30,20 +30,20 @@ pub enum JSONRPCMessage {
 
 /// A request that expects a response.
 #[derive(Debug, Clone, PartialEq, Deserialize, Serialize, JsonSchema, TS)]
-#[ts(optional_fields = nullable)]
 pub struct JSONRPCRequest {
     pub id: RequestId,
     pub method: String,
     #[serde(default, skip_serializing_if = "Option::is_none")]
+    #[ts(optional)]
     pub params: Option<serde_json::Value>,
 }
 
 /// A notification which does not expect a response.
 #[derive(Debug, Clone, PartialEq, Deserialize, Serialize, JsonSchema, TS)]
-#[ts(optional_fields = nullable)]
 pub struct JSONRPCNotification {
     pub method: String,
     #[serde(default, skip_serializing_if = "Option::is_none")]
+    #[ts(optional)]
     pub params: Option<serde_json::Value>,
 }
 
@@ -62,10 +62,10 @@ pub struct JSONRPCError {
 }
 
 #[derive(Debug, Clone, PartialEq, Deserialize, Serialize, JsonSchema, TS)]
-#[ts(optional_fields = nullable)]
 pub struct JSONRPCErrorError {
     pub code: i64,
     #[serde(default, skip_serializing_if = "Option::is_none")]
+    #[ts(optional)]
     pub data: Option<serde_json::Value>,
     pub message: String,
 }