Use native Codex steering and transcript deletion

server/src/config.rs

@@ -156,8 +156,7 @@ pub enum DriverKind {
     /// The Claude Code CLI over stream-json. Named for the CLI specifically:
     /// bare "claude" would suggest the credit-billed API, which this is not.
     ClaudeCli,
-    /// The Codex CLI's `exec --json` JSONL stream. Each process is one turn;
-    /// the thread id it reports is resumed by the next process.
+    /// The Codex CLI's persistent app-server JSONL protocol.
     CodexCli,
 }
 
@@ -235,9 +234,18 @@ impl DriverKind {
     /// the one sentence that has to be true: said of a session that can in fact
     /// be brought back, it spends the credibility the warning needs.
     pub fn keeps_own_transcript(self) -> bool {
+        self.own_transcript_name().is_some()
+    }
+
+    /// The product whose durable transcript survives an ordinary app delete.
+    /// Reported to the phone because a provider's configured name is not the
+    /// name of its storage, and calling Codex's rollout a Claude transcript is
+    /// especially misleading on an irreversible switch.
+    pub fn own_transcript_name(self) -> Option<&'static str> {
         match self {
-            Self::ClaudeCli | Self::CodexCli => true,
-            Self::Echo | Self::LlamaCpp => false,
+            Self::ClaudeCli => Some("Claude Code"),
+            Self::CodexCli => Some("Codex"),
+            Self::Echo | Self::LlamaCpp => None,
         }
     }