fix WebSearchAction type clash between v1 and v2 (#10408)

type clash; app-server generated types were still using the v1
snake_case `WebSearchAction`, so there was a mismatch between the
camelCase emitted types and the snake_case types we were trying to
parse.

Updated v2 `WebSearchAction` to export into the `v2/` type set and
updated `ThreadItem` to use that.

### Tests
Ran new `just write-app-server-schema` to surface changes to schema, the
import looks correct now.

codex-rs/app-server-protocol/src/protocol/v2.rs

@@ -2170,6 +2170,7 @@ pub enum ThreadItem {
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq, JsonSchema, TS)]
 #[serde(tag = "type", rename_all = "camelCase")]
 #[ts(tag = "type", rename_all = "camelCase")]
+#[ts(export_to = "v2/")]
 pub enum WebSearchAction {
     Search {
         query: Option<String>,