bxctl: chat_approvals' helper accepts a broken pipe on stdin

json_prints_only_json_and_never_asks_brokerd failed once under load: the helper wrote the typed
input to a `bxctl chat --json` that never reads stdin and had already exited, and unwrapped the
broken pipe. A broken pipe on that write is now accepted; any other error still fails the test,
and a test whose input must be read checks the output.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

docs/plans/M5c2/README.md

@@ -104,13 +104,11 @@ The gate count is the passed total of `cargo test --workspace` plus one, for the
 | 05 | 1403 | 24, 24 |
 | 06 | 1414 | 22, 22 |
 
-**Known flaky test** (T52): `bxctl`'s `chat_approvals` test
+**A flaky test, fixed before the run:** `bxctl`'s `chat_approvals` test
 `json_prints_only_json_and_never_asks_brokerd` failed once in 5 loaded runs of the whole workspace
-while task 06 was checked (and 0 in 60 runs of that file alone under load). It writes to the
-standard input of a `bxctl chat --say` that does not read it and may already have exited, and
-`write_all` fails with a broken pipe. No task of this plan touches `bxctl`'s chat. A session
-that sees it fail once, then pass on a rerun and in the gate, names it in its row's Notes and
-goes on.
+while task 06 was checked: its helper wrote to the standard input of a `bxctl chat` that does not
+read it and may already have exited, and unwrapped the broken pipe. The helper now accepts a
+broken pipe on that write (master, after task 06); 0 failures in 100 loaded runs.
 
 ## Before hand-over