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/v2/ThreadListParams.json

@@ -0,0 +1,85 @@
+{
+  "$schema": "http://json-schema.org/draft-07/schema#",
+  "definitions": {
+    "ThreadSortKey": {
+      "enum": [
+        "created_at",
+        "updated_at"
+      ],
+      "type": "string"
+    },
+    "ThreadSourceKind": {
+      "enum": [
+        "cli",
+        "vscode",
+        "exec",
+        "appServer",
+        "subAgent",
+        "subAgentReview",
+        "subAgentCompact",
+        "subAgentThreadSpawn",
+        "subAgentOther",
+        "unknown"
+      ],
+      "type": "string"
+    }
+  },
+  "properties": {
+    "archived": {
+      "description": "Optional archived filter; when set to true, only archived threads are returned. If false or null, only non-archived threads are returned.",
+      "type": [
+        "boolean",
+        "null"
+      ]
+    },
+    "cursor": {
+      "description": "Opaque pagination cursor returned by a previous call.",
+      "type": [
+        "string",
+        "null"
+      ]
+    },
+    "limit": {
+      "description": "Optional page size; defaults to a reasonable server-side value.",
+      "format": "uint32",
+      "minimum": 0.0,
+      "type": [
+        "integer",
+        "null"
+      ]
+    },
+    "modelProviders": {
+      "description": "Optional provider filter; when set, only sessions recorded under these providers are returned. When present but empty, includes all providers.",
+      "items": {
+        "type": "string"
+      },
+      "type": [
+        "array",
+        "null"
+      ]
+    },
+    "sortKey": {
+      "anyOf": [
+        {
+          "$ref": "#/definitions/ThreadSortKey"
+        },
+        {
+          "type": "null"
+        }
+      ],
+      "description": "Optional sort key; defaults to created_at."
+    },
+    "sourceKinds": {
+      "description": "Optional source filter; when set, only sessions from these source kinds are returned. When omitted or empty, defaults to interactive sources.",
+      "items": {
+        "$ref": "#/definitions/ThreadSourceKind"
+      },
+      "type": [
+        "array",
+        "null"
+      ]
+    }
+  },
+  "title": "ThreadListParams",
+  "type": "object"
+}