permissions: make runtime config profile-backed (#19606)

## Why

This supersedes #19391. During stack repair, GitHub marked #19391 as
merged into a temporary stack branch rather than into `main`, so the
runtime-config change needed a fresh PR.

`PermissionProfile` is now the canonical permissions shape after #19231
because it can distinguish `Managed`, `Disabled`, and `External`
enforcement while also carrying filesystem rules that legacy
`SandboxPolicy` cannot represent cleanly. Core config and session state
still needed to accept profile-backed permissions without forcing every
profile through the strict legacy bridge, which rejected valid runtime
profiles such as direct write roots.

The unrelated CI/test hardening that previously rode along with this PR
has been split into #19683 so this PR stays focused on the permissions
model migration.

## What Changed

- Adds `Permissions.permission_profile` and
`SessionConfiguration.permission_profile` as constrained runtime state,
while keeping `sandbox_policy` as a legacy compatibility projection.
- Introduces profile setters that keep `PermissionProfile`, split
filesystem/network policies, and legacy `SandboxPolicy` projections
synchronized.
- Uses a compatibility projection for requirement checks and legacy
consumers instead of rejecting profiles that cannot round-trip through
`SandboxPolicy` exactly.
- Updates config loading, config overrides, session updates, turn
context plumbing, prompt permission text, sandbox tags, and exec request
construction to carry profile-backed runtime permissions.
- Preserves configured deny-read entries and `glob_scan_max_depth` when
command/session profiles are narrowed.
- Adds `PermissionProfile::read_only()` and
`PermissionProfile::workspace_write()` presets that match legacy
defaults.

## Verification

- `cargo test -p codex-core direct_write_roots`
- `cargo test -p codex-core runtime_roots_to_legacy_projection`
- `cargo test -p codex-app-server
requested_permissions_trust_project_uses_permission_profile_intent`




---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/19606).
* #19395
* #19394
* #19393
* #19392
* __->__ #19606

codex-rs/analytics/src/analytics_client_tests.rs

@@ -161,7 +161,7 @@ fn sample_thread_start_response(thread_id: &str, ephemeral: bool, model: &str) -
 }
 
 fn sample_permission_profile() -> AppServerPermissionProfile {
-    CorePermissionProfile::from_legacy_sandbox_policy(&SandboxPolicy::DangerFullAccess).into()
+    CorePermissionProfile::Disabled.into()
 }
 
 fn sample_app_server_client_metadata() -> CodexAppServerClientMetadata {