[codex] Add unsandboxed process exec API (#19040)

## Why

App-server clients sometimes need argv-based local process execution
while sandbox policy is controlled outside Codex. Those environments can
reject sandbox-disabling paths before a command ever starts, even when
the caller intentionally wants unsandboxed execution.

This PR adds a distinct `process/*` API for that use case instead of
extending `command/exec` with another sandbox-disabling shape. Keeping
the new surface separate also makes the future removal of `command/exec`
simpler: clients that need explicit process lifecycle control can move
to the newer handle-based API without depending on `command/exec`
business logic.

## What changed

- Added v2 process lifecycle methods: `process/spawn`,
`process/writeStdin`, `process/resizePty`, and `process/kill`.
- Added process notifications: `process/outputDelta` for streamed
stdout/stderr chunks and `process/exited` for final exit status and
buffered output.
- Made `process/spawn` intentionally unsandboxed and omitted
sandbox-selection fields such as `sandboxPolicy` and
`permissionProfile`.
- Added client-supplied, connection-scoped `processHandle` values for
follow-up control requests and notification routing.
- Supported cwd, environment overrides, PTY mode and size, stdin
streaming, stdout/stderr streaming, per-stream output caps, and timeout
controls.
- Killed active process sessions when the originating app-server
connection closes.
- Wired the implementation through the modular `request_processors/`
app-server layout, with process-handle request serialization for
follow-up control calls.
- Updated generated JSON/TypeScript schema fixtures and documented the
new API in `codex-rs/app-server/README.md`.
- Added v2 app-server integration coverage in
`codex-rs/app-server/tests/suite/v2/process_exec.rs` for spawn
acknowledgement before exit, buffered output caps, and process
termination.

## Verification

- `cargo test -p codex-app-server-protocol`
- `cargo test -p codex-app-server`

---------

Co-authored-by: Owen Lin <owen@openai.com>

codex-rs/tui/src/app/app_server_event_targets.rs

@@ -153,6 +153,8 @@ pub(super) fn server_notification_thread_target(
         | ServerNotification::FuzzyFileSearchSessionUpdated(_)
         | ServerNotification::FuzzyFileSearchSessionCompleted(_)
         | ServerNotification::CommandExecOutputDelta(_)
+        | ServerNotification::ProcessOutputDelta(_)
+        | ServerNotification::ProcessExited(_)
         | ServerNotification::FsChanged(_)
         | ServerNotification::WindowsWorldWritableWarning(_)
         | ServerNotification::WindowsSandboxSetupCompleted(_)