app-server: drop legacy profile config surface (#24067)

## Why

Legacy `[profiles.<name>]` config tables and the legacy `profile`
selector are being retired in favor of profile files selected with
`--profile <name>`. After #23886 removed the CLI-side legacy profile
plumbing, the app-server config surface still exposed those fields and
still carried conversion code for the old protocol shape.

## What changed

- Remove `profile`, `profiles`, and `ProfileV2` from the app-server
config protocol/schema output so `config/read` no longer returns legacy
profile config.
- Drop the old v1 `UserSavedConfig` profile conversion path from
`config`.
- Reject new app-server config writes under `profiles.*` with the same
migration direction used for `profile`, while still allowing callers to
clear existing legacy profile tables.
- Refresh app-server config coverage and the experimental API README
example around the remaining `Config` nesting path.

## Verification

- Added config-manager coverage that `config/read` omits legacy profile
config, `profiles.*` writes are rejected, and existing legacy profile
tables can still be cleared.
- Updated the v2 config RPC test to cover the rejected `profiles.*`
batch-write path.

codex-rs/app-server-protocol/src/protocol/v1.rs

@@ -209,20 +209,6 @@ pub struct UserSavedConfig {
     pub model_reasoning_summary: Option<ReasoningSummary>,
     pub model_verbosity: Option<Verbosity>,
     pub tools: Option<Tools>,
-    pub profile: Option<String>,
-    pub profiles: HashMap<String, Profile>,
-}
-
-#[derive(Deserialize, Debug, Clone, PartialEq, Serialize, JsonSchema, TS)]
-#[serde(rename_all = "camelCase")]
-pub struct Profile {
-    pub model: Option<String>,
-    pub model_provider: Option<String>,
-    pub approval_policy: Option<AskForApproval>,
-    pub model_reasoning_effort: Option<ReasoningEffort>,
-    pub model_reasoning_summary: Option<ReasoningSummary>,
-    pub model_verbosity: Option<Verbosity>,
-    pub chatgpt_base_url: Option<String>,
 }
 
 #[derive(Deserialize, Debug, Clone, PartialEq, Serialize, JsonSchema, TS)]