[1 of 4] tui: route primary settings writes through app server (#22913)

## Why
The TUI can run against a remote app server, but several high-traffic
settings still persisted by editing the local config file. That sends
remote sessions' preference writes to the wrong machine and lets local
disk state drift from the app-server-owned config.

This is **[1 of 4]** in a stacked series that moves TUI-owned config
mutations onto app-server APIs.

## What changed
- Added a small TUI helper for typed app-server config writes.
- Routed primary interactive preference writes through
`config/batchWrite`.
- Preserved existing profile scoping for settings that already support
`profiles.<profile>.*` overrides.

## Config keys affected
- `model`
- `model_reasoning_effort`
- `personality`
- `service_tier`
- `plan_mode_reasoning_effort`
- `approvals_reviewer`
- `notice.fast_default_opt_out`
- Profile-scoped equivalents under `profiles.<profile>.*`

## Suggested manual validation
- Connect the TUI to a remote app server, change `model` and
`model_reasoning_effort`, reconnect, and confirm the remote config
retained both values while the local `config.toml` did not change.
- Change `personality`, `plan_mode_reasoning_effort`, and the explicit
auto-review selection, then reconnect and confirm those choices persist
through the app server.
- Clear the service tier back to default and confirm `service_tier` is
cleared while `notice.fast_default_opt_out = true` is persisted
remotely.
- Repeat one setting change with an active profile and confirm the write
lands under `profiles.<profile>.*`.

## Stack
1. [#22913](https://github.com/openai/codex/pull/22913) `[1 of 4]`
primary settings writes
2. [#22914](https://github.com/openai/codex/pull/22914) `[2 of 4]` app
and skill enablement
3. [#22915](https://github.com/openai/codex/pull/22915) `[3 of 4]`
feature and memory toggles
4. [#22916](https://github.com/openai/codex/pull/22916) `[4 of 4]`
startup and onboarding bookkeeping

codex-rs/app-server/tests/suite/v2/config_rpc.rs

@@ -893,6 +893,71 @@ async fn config_batch_write_applies_multiple_edits() -> Result<()> {
     Ok(())
 }
 
+#[tokio::test(flavor = "multi_thread", worker_threads = 2)]
+async fn config_batch_write_preserves_dotted_profile_names() -> Result<()> {
+    let tmp_dir = TempDir::new()?;
+    let codex_home = tmp_dir.path().canonicalize()?;
+    write_config(
+        &tmp_dir,
+        r#"
+profile = "team.prod"
+
+[profiles."team.prod"]
+model = "gpt-5.3-spark"
+
+[profiles.team.prod]
+model = "should-stay-put"
+"#,
+    )?;
+
+    let mut mcp = McpProcess::new(&codex_home).await?;
+    timeout(DEFAULT_READ_TIMEOUT, mcp.initialize()).await??;
+
+    let batch_id = mcp
+        .send_config_batch_write_request(ConfigBatchWriteParams {
+            file_path: Some(codex_home.join("config.toml").display().to_string()),
+            edits: vec![
+                ConfigEdit {
+                    key_path: "profiles.\"team.prod\".model".to_string(),
+                    value: json!("gpt-5.5"),
+                    merge_strategy: MergeStrategy::Replace,
+                },
+                ConfigEdit {
+                    key_path: "items.sample@catalog.enabled".to_string(),
+                    value: json!(true),
+                    merge_strategy: MergeStrategy::Replace,
+                },
+            ],
+            expected_version: None,
+            reload_user_config: false,
+        })
+        .await?;
+    let batch_resp: JSONRPCResponse = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.read_stream_until_response_message(RequestId::Integer(batch_id)),
+    )
+    .await??;
+    let batch_write: ConfigWriteResponse = to_response(batch_resp)?;
+    assert_eq!(batch_write.status, WriteStatus::Ok);
+
+    let config: toml::Value =
+        toml::from_str(&std::fs::read_to_string(codex_home.join("config.toml"))?)?;
+    assert_eq!(
+        config["profiles"]["team.prod"]["model"].as_str(),
+        Some("gpt-5.5")
+    );
+    assert_eq!(
+        config["profiles"]["team"]["prod"]["model"].as_str(),
+        Some("should-stay-put")
+    );
+    assert_eq!(
+        config["items"]["sample@catalog"]["enabled"].as_bool(),
+        Some(true)
+    );
+
+    Ok(())
+}
+
 #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
 async fn config_batch_write_updates_multiple_desktop_settings() -> Result<()> {
     let tmp_dir = TempDir::new()?;