[codex-rs] Add writes app approval mode (#30482)

## Summary

- Adds `writes` to `AppToolApproval` and exposes it through config and
app-server schemas, including
`[apps._default].default_tools_approval_mode`.
- In `writes`, tools with `readOnlyHint = true` skip approval; all other
tools prompt, including non-destructive writes and tools without
annotations.
- Prevents session or persistent approval choices in this mode so later
writes still prompt.

## Why

`auto` only prompts for risk-hinted actions, while `prompt` also
interrupts reads. Apps need a middle mode that gates writes without
prompting for declared read-only actions.

## Validation

- `just write-config-schema`
- `just write-app-server-schema`
- `just fmt`
- `just test -p codex-core mcp_turn_metadata` (4 passed)
- `just test -p codex-core writes_mode` (2 passed)
- `just test -p codex-app-server config_read_includes_apps` (1 passed)
- `just test -p codex-app-server-protocol` (251 passed)
- `just test -p codex-config` (200 passed)
- `just test -p codex-cli` (300 passed)
- `just fix -p codex-core -p codex-config -p codex-app-server-protocol
-p codex-app-server -p codex-cli`

codex-rs/app-server-protocol/src/protocol/v2/config.rs

@@ -163,6 +163,7 @@ pub struct AnalyticsConfig {
 pub enum AppToolApproval {
     Auto,
     Prompt,
+    Writes,
     Approve,
 }