[operator] Count dictation completions in value probe

[r3dbars]

Summary

• include existing successful dictation completions in the PostHog first-value health probe
• update the ops credential docs to match the probe shape
• add a repo contract check so the probe and docs stay aligned

Verification

• TRANSCRIPTED_DISABLE_FILE_LOGGER=1 bash run-tests.sh
• bash scripts/ops/health-probe.sh posthog

Nightly context

Open automation drafts checked before editing: #911 and #912. This avoids both surfaces.

[r3dbars]

verdict: no-findings-but-human

Reviewed head ad9254077d3adac87d966ee8c6a6b03f37628357. Findings: one weak contract assertion found and fixed.

Actions: pushed ad925407 (Tighten PostHog first-value probe contract) so the test now checks the first_value_events assignment itself. Human signoff because this is a draft PR and touches PostHog ops telemetry.

Checks: reviewed PR metadata, discussion, diff, and status checks; repo-hygiene is passing; read repo/test/script guidance; ran scripts/dev/agent-preflight.sh, bash -n scripts/ops/health-probe.sh, git diff --check, TRANSCRIPTED_DISABLE_FILE_LOGGER=1 bash build-deps.sh --force, TRANSCRIPTED_DISABLE_FILE_LOGGER=1 bash build.sh --no-open, and TRANSCRIPTED_DISABLE_FILE_LOGGER=1 bash run-tests.sh (3035 passed).

manual_merge_handoff:
head_sha: ad92540
verdict: no-findings-but-human
blockers: draft PR and PostHog ops telemetry human signoff
checks: gh pr view/diff/checks, repo-hygiene passing, preflight, bash -n health probe, git diff --check, build-deps --force, build, run-tests