config: remove legacy profile write paths (#24055)

## Why

[#23883](https://github.com/openai/codex/pull/23883) moved the
user-facing `--profile` flag onto profile v2 and
[#23886](https://github.com/openai/codex/pull/23886) removed CLI
forwarding for the legacy profile-v1 path. Core and TUI config
persistence still carried `active_profile` and
`ConfigEditsBuilder::with_profile`, which let later writes continue
targeting legacy `[profiles.<name>]` tables after profile selection
moved to profile-v2 config files.

## What

- Remove legacy profile routing from
[`ConfigEditsBuilder`](https://github.com/openai/codex/blob/4b38e9c22e762261d7f7eef49d8a21792e241a06/codex-rs/core/src/config/edit.rs#L1064-L1294),
so core config edits no longer carry `with_profile` or infer
`[profiles.*]` write targets from a `profile` key.
- Drop `active_profile` plumbing from runtime `Config`, TUI
startup/state, app-server config override forwarding, and Windows
sandbox setup persistence.
- Make app-server-backed TUI config edits use unscoped model,
service-tier, feature, Auto-review, plan-mode, and Windows sandbox paths
through
[`tui/src/config_update.rs`](https://github.com/openai/codex/blob/4b38e9c22e762261d7f7eef49d8a21792e241a06/codex-rs/tui/src/config_update.rs#L43-L112).
- Update config edit coverage so legacy `profile` state stays untouched
by direct model writes, and remove tests whose only contract was the
deleted profile-scoped persistence path.

## Testing

- Not run locally.

codex-rs/exec/src/lib.rs

@@ -134,7 +134,6 @@ pub use exec_events::TurnStartedEvent;
 pub use exec_events::Usage;
 pub use exec_events::WebSearchItem;
 use serde_json::Value;
-use std::collections::HashMap;
 use std::io::IsTerminal;
 use std::io::Read;
 use std::path::Path;
@@ -967,7 +966,7 @@ fn thread_start_params_from_config(config: &Config) -> ThreadStartParams {
         approvals_reviewer: approvals_reviewer_override_from_config(config),
         sandbox: sandbox.flatten(),
         permissions,
-        config: config_request_overrides_from_config(config),
+        config: None,
         ephemeral: Some(config.ephemeral),
         thread_source: Some(ThreadSource::User),
         ..ThreadStartParams::default()
@@ -998,7 +997,7 @@ fn thread_resume_params_from_config(config: &Config, thread_id: String) -> Threa
         approvals_reviewer: approvals_reviewer_override_from_config(config),
         sandbox: sandbox.flatten(),
         permissions,
-        config: config_request_overrides_from_config(config),
+        config: None,
         ..ThreadResumeParams::default()
     }
 }
@@ -1039,13 +1038,6 @@ fn sandbox_mode_from_permission_profile(
     }
 }
 
-fn config_request_overrides_from_config(config: &Config) -> Option<HashMap<String, Value>> {
-    config
-        .active_profile
-        .as_ref()
-        .map(|profile| HashMap::from([("profile".to_string(), Value::String(profile.clone()))]))
-}
-
 fn approvals_reviewer_override_from_config(
     config: &Config,
 ) -> Option<codex_app_server_protocol::ApprovalsReviewer> {