[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/parse_command.rs

@@ -18,14 +18,11 @@ pub enum ParsedCommand {
     },
     ListFiles {
         cmd: String,
-        #[ts(optional = nullable)]
         path: Option<String>,
     },
     Search {
         cmd: String,
-        #[ts(optional = nullable)]
         query: Option<String>,
-        #[ts(optional = nullable)]
         path: Option<String>,
     },
     Unknown {