feat: vendor app-server protocol schema fixtures (#10371)

Similar to what @sayan-oai did in openai/codex#8956 for
`config.schema.json`, this PR updates the repo so that it includes the
output of `codex app-server generate-json-schema` and `codex app-server
generate-ts` and adds a test to verify it is in sync with the current
code.

Motivation:
- This makes any schema changes introduced by a PR transparent during
code review.
- In particular, this should help us catch PRs that would introduce a
non-backwards-compatible change to the app schema (eventually, this
should also be enforced by tooling).
- Once https://github.com/openai/codex/pull/10231 is in to formalize the
notion of "experimental" fields, we can work on ensuring the
non-experimental bits are backwards-compatible.

`codex-rs/app-server-protocol/tests/schema_fixtures.rs` was added as the
test and `just write-app-server-schema` can be use to generate the
vendored schema files.

Incidentally, when I run:

```
rg _ codex-rs/app-server-protocol/schema/typescript/v2
```

I see a number of `snake_case` names that should be `camelCase`.

codex-rs/app-server-protocol/schema/json/ToolRequestUserInputParams.json

@@ -0,0 +1,84 @@
+{
+  "$schema": "http://json-schema.org/draft-07/schema#",
+  "definitions": {
+    "ToolRequestUserInputOption": {
+      "description": "EXPERIMENTAL. Defines a single selectable option for request_user_input.",
+      "properties": {
+        "description": {
+          "type": "string"
+        },
+        "label": {
+          "type": "string"
+        }
+      },
+      "required": [
+        "description",
+        "label"
+      ],
+      "type": "object"
+    },
+    "ToolRequestUserInputQuestion": {
+      "description": "EXPERIMENTAL. Represents one request_user_input question and its required options.",
+      "properties": {
+        "header": {
+          "type": "string"
+        },
+        "id": {
+          "type": "string"
+        },
+        "isOther": {
+          "default": false,
+          "type": "boolean"
+        },
+        "isSecret": {
+          "default": false,
+          "type": "boolean"
+        },
+        "options": {
+          "items": {
+            "$ref": "#/definitions/ToolRequestUserInputOption"
+          },
+          "type": [
+            "array",
+            "null"
+          ]
+        },
+        "question": {
+          "type": "string"
+        }
+      },
+      "required": [
+        "header",
+        "id",
+        "question"
+      ],
+      "type": "object"
+    }
+  },
+  "description": "EXPERIMENTAL. Params sent with a request_user_input event.",
+  "properties": {
+    "itemId": {
+      "type": "string"
+    },
+    "questions": {
+      "items": {
+        "$ref": "#/definitions/ToolRequestUserInputQuestion"
+      },
+      "type": "array"
+    },
+    "threadId": {
+      "type": "string"
+    },
+    "turnId": {
+      "type": "string"
+    }
+  },
+  "required": [
+    "itemId",
+    "questions",
+    "threadId",
+    "turnId"
+  ],
+  "title": "ToolRequestUserInputParams",
+  "type": "object"
+}