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/agent-identity/src/lib.rs

@@ -322,6 +322,7 @@ pub fn build_abom(session_source: SessionSource) -> AgentBillOfMaterials {
             | SessionSource::Exec
             | SessionSource::Mcp
             | SessionSource::Custom(_)
+            | SessionSource::Internal(_)
             | SessionSource::SubAgent(_)
             | SessionSource::Unknown => "codex-cli".to_string(),
         },