core tests: submit turns with permission profiles (#20010)

## Summary

- Add `PermissionProfile`-based turn submission helpers to
`core_test_support`, while keeping the legacy `SandboxPolicy` helper for
tests that intentionally exercise legacy fallback behavior.
- Switch the default `TestCodex::submit_turn()` path to send a real
`PermissionProfile` plus the required legacy compatibility projection in
`Op::UserTurn`.
- Migrate straightforward app/search/shell/truncation tests from
`SandboxPolicy::{DangerFullAccess, ReadOnly}` to
`PermissionProfile::{Disabled, read_only}`.
- Add a TUI compatibility projection helper for legacy app-server fields
so non-legacy writable roots are preserved instead of being downgraded
to read-only.
- Fix remote start/resume/fork sandbox-mode projection to classify any
managed profile with writable roots as workspace-write, not only
profiles that can write `cwd`.
- Reduce `SandboxPolicy` references in `codex-rs/core/tests` from 47
files to 41 files without changing production behavior.

## Testing

- `cargo check -p codex-core --tests`
- `cargo test -p codex-tui
compatibility_profile_preserves_unbridgeable_write_roots`
- `cargo test -p codex-tui
sandbox_mode_preserves_non_cwd_write_roots_for_remote_sessions`
- `just fmt`
- `just fix -p core_test_support`
- `just fix -p codex-core`

codex-rs/core/tests/suite/tool_suggest.rs

@@ -8,8 +8,8 @@ use codex_core::config::Config;
 use codex_features::Feature;
 use codex_login::CodexAuth;
 use codex_models_manager::bundled_models_response;
+use codex_protocol::models::PermissionProfile;
 use codex_protocol::protocol::AskForApproval;
-use codex_protocol::protocol::SandboxPolicy;
 use core_test_support::apps_test_server::AppsTestServer;
 use core_test_support::responses::ev_assistant_message;
 use core_test_support::responses::ev_completed;
@@ -111,10 +111,10 @@ async fn tool_suggest_is_available_without_search_tool_after_discovery_attempts(
         });
     let test = builder.build(&server).await?;
 
-    test.submit_turn_with_policies(
+    test.submit_turn_with_approval_and_permission_profile(
         "list tools",
         AskForApproval::Never,
-        SandboxPolicy::DangerFullAccess,
+        PermissionProfile::Disabled,
     )
     .await?;