Remove first-party type from app metadata (#34844)

## What changed

Remove `first_party_type` from connector app metadata and the app-server v2
protocol. Update metadata conversion and merge paths, generated JSON and
TypeScript schemas, and affected test fixtures to match.

GitOrigin-RevId: 3f2e56eca68352360d8c0d99d48486ae65d664c1

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

@@ -107,7 +107,6 @@ pub struct AppMetadata {
     pub version: Option<String>,
     pub version_id: Option<String>,
     pub version_notes: Option<String>,
-    pub first_party_type: Option<String>,
     pub first_party_requires_install: Option<bool>,
     pub show_in_composer_when_unlinked: Option<bool>,
 }