fix(coding-agent): process idle ctx.shutdown() requests in RPC mode (#11746)

In RPC mode, `shutdownHandler` only set a `shutdownRequested` flag. That
flag was checked in two places: after a stdin command was handled and on
`agent_settled`. If an extension called `ctx.shutdown()` while the
session was idle (for example from a timer), neither check ever ran. The
process stayed alive until the client sent another command. Interactive
mode already shuts down right away in this case.

Changes in `packages/coding-agent/src/modes/rpc/rpc-mode.ts`:
- **One check for all paths:** `checkShutdownRequested()` shuts down
only when a request is pending, input is attached, no command is being
handled, and the session is idle. Each of those ending calls it again:
command completion, prompt settle, `agent_settled`, and input attach.
- **Idle requests:** the shutdown handler schedules the check on the
next tick, so the requesting handler finishes first. The conditions are
checked when the tick runs, not when it is scheduled: a stdin command
that arrives in between is handled first, and shutdown follows when it
finishes.
- **Requests during startup:** a request made before input is attached
(for example a synchronous `ctx.shutdown()` in `session_start`) is
checked once the input reader is attached.
- **Requests during a command:** shutdown waits until the command
finishes, including extension commands. A `prompt` command returns
before `session.prompt()` settles, so it stays counted as in flight
until the prompt settles, and the shutdown check runs then. This also
fixes an existing ordering problem: an extension command that called
`ctx.shutdown()` could exit the process before its `prompt` response was
written.
- **Repeated requests:** `checkShutdownRequested()` does nothing once
shutdown has started, so a second `ctx.shutdown()` does not call
`process.exit` in the middle of async cleanup. A second stdin EOF or
signal still forces exit, as before.

Shutdown requested during a running turn is still handled on
`agent_settled`, as before. A request made while an extension-started
compaction runs (not idle, no run to settle) still waits for the next
command or run; `docs/rpc.md` and `docs/extensions.md` note this.

Docs (`docs/rpc.md`, `docs/extensions.md`) and the CHANGELOG are
updated.

## Testing
- Added three tests to `test/rpc-prompt-response-semantics.test.ts`:
  - an async `ctx.shutdown()` on an idle session exits;
- an extension command that calls `ctx.shutdown()` gets its `prompt`
response written before exit;
- a command that arrives after an idle request but before the scheduled
check runs gets its response written before exit.

  All three fail without the change and pass with it.
- `npm run check` passes. All `test/rpc*` tests pass.
- In `./test.sh`, all coding-agent tests pass. The only failures were
timeouts in durable/harness tests (`store-storage`, `tools-images`,
connection close), which this change does not touch.
- Reproduction from the issue: run `pi --mode rpc --no-session -ne -e
./shutdown-probe.mjs` with stdin held open and nothing sent.
- Before the change, the process stayed alive until a timeout killed it
(exit 124).
- After the change, `session_shutdown` fires and the process exits with
code 0.
- A synchronous `ctx.shutdown()` in `session_start` also exits with code
0.

Fixes #11599

Requested by @petrroll

---------

Co-authored-by: triagent <triagent@localhost>
Co-authored-by: Petr Houška <houskape@gmail.com>

packages/coding-agent/docs/rpc.md

@@ -92,7 +92,7 @@ Clients must also handle child-process startup failures, unexpected exits, stder
 
 Close the child's stdin to request an orderly shutdown. Pi disposes the active runtime before exiting. Clients should still handle process signals and unexpected exits.
 
-An extension can also request shutdown through its extension context. Pi completes shutdown after the current command or after the active run emits `agent_settled`.
+An extension can also request shutdown with `ctx.shutdown()`. If the session is idle and no command is being handled, Pi shuts down right away. Otherwise it shuts down once the current command finishes (for `prompt`, once the prompt settles) or the active run emits `agent_settled`. (A request made while an extension-started compaction is running waits for the next command or run to finish.)
 
 ## Minimal client