Add in-process app server and wire up exec to use it (#14005)

This is a subset of PR #13636. See that PR for a full overview of the
architectural change.

This PR implements the in-process app server and modifies the
non-interactive "exec" entry point to use the app server.

---------

Co-authored-by: Felipe Coury <felipe.coury@gmail.com>

codex-rs/app-server-client/README.md

@@ -0,0 +1,67 @@
+# codex-app-server-client
+
+Shared in-process app-server client used by conversational CLI surfaces:
+
+- `codex-exec`
+- `codex-tui`
+
+## Purpose
+
+This crate centralizes startup and lifecycle management for an in-process
+`codex-app-server` runtime, so CLI clients do not need to duplicate:
+
+- app-server bootstrap and initialize handshake
+- in-memory request/event transport wiring
+- lifecycle orchestration around caller-provided startup identity
+- graceful shutdown behavior
+
+## Startup identity
+
+Callers pass both the app-server `SessionSource` and the initialize
+`client_info.name` explicitly when starting the facade.
+
+That keeps thread metadata (for example in `thread/list` and `thread/read`)
+aligned with the originating runtime without baking TUI/exec-specific policy
+into the shared client layer.
+
+## Transport model
+
+The in-process path uses typed channels:
+
+- client -> server: `ClientRequest` / `ClientNotification`
+- server -> client: `InProcessServerEvent`
+  - `ServerRequest`
+  - `ServerNotification`
+  - `LegacyNotification`
+
+JSON serialization is still used at external transport boundaries
+(stdio/websocket), but the in-process hot path is typed.
+
+Typed requests still receive app-server responses through the JSON-RPC
+result envelope internally. That is intentional: the in-process path is
+meant to preserve app-server semantics while removing the process
+boundary, not to introduce a second response contract.
+
+## Bootstrap behavior
+
+The client facade starts an already-initialized in-process runtime, but
+thread bootstrap still follows normal app-server flow:
+
+- caller sends `thread/start` or `thread/resume`
+- app-server returns the immediate typed response
+- richer session metadata may arrive later as a `SessionConfigured`
+  legacy event
+
+Surfaces such as TUI and exec may therefore need a short bootstrap
+phase where they reconcile startup response data with later events.
+
+## Backpressure and shutdown
+
+- Queues are bounded and use `DEFAULT_IN_PROCESS_CHANNEL_CAPACITY` by default.
+- Full queues return explicit overload behavior instead of unbounded growth.
+- `shutdown()` performs a bounded graceful shutdown and then aborts if timeout
+  is exceeded.
+
+If the client falls behind on event consumption, the worker emits
+`InProcessServerEvent::Lagged` and may reject pending server requests so
+approval flows do not hang indefinitely behind a saturated queue.