fix(ops): make the alert steps actually run - #143

Run 30798868809 detected a real outage and told nobody. The publication
heartbeat correctly exited 1 after 101 hours without a new post, and the
delivery step was skipped.

GitHub's default shell is `bash --noprofile --norc -eo pipefail`, which already
sets -e. The steps declared `set -uo pipefail`, which adds -u but does not
remove -e, so the non-zero exit aborted the step before `code=$?` and the
`echo "exit_code=..." >> $GITHUB_OUTPUT` ever ran. The delivery step guards on
`steps.<id>.outputs.exit_code != ''`, which was therefore false, so it skipped.

The check worked. The notification never existed. That is precisely the failure
mode this monitoring was built to eliminate, reintroduced one layer up.

The same run shows a second defect: the release-state check was skipped too,
because a failed heartbeat aborted the remaining steps. One broken check hid
whatever else was wrong.

Disable errexit around each measurement so the code is recorded, and let the
checks run independently of each other.

Four tests pin both properties, since the symptom of getting this wrong is
silence — which is indistinguishable from health, and cannot be noticed by
watching.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>