feat: split memories part 2 (#19860)

Keep extracting memories out of core and moving the write trigger in the
app-server
This is temporary and it should move at the client level as a follow-up
This makes core fully independant from `codex-memories-write`

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Co-authored-by: Codex <noreply@openai.com>

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

@@ -1996,6 +1996,8 @@ impl From<CoreSessionSource> for SessionSource {
             CoreSessionSource::Exec => SessionSource::Exec,
             CoreSessionSource::Mcp => SessionSource::AppServer,
             CoreSessionSource::Custom(source) => SessionSource::Custom(source),
+            // We do not want to render those at the app-server level.
+            CoreSessionSource::Internal(_) => SessionSource::Unknown,
             CoreSessionSource::SubAgent(sub) => SessionSource::SubAgent(sub),
             CoreSessionSource::Unknown => SessionSource::Unknown,
         }