Ask a team whether their new automation is working and you will get a feeling. Feelings are a bad dashboard.
Three numbers, collected for a month, will tell you more about an automation than any demo. None of them require instrumentation beyond what you already have.
Hours returned per week
Take one repeated task. Time it by hand for a week before automating, including the review pass. Then time the automated version the same way. The delta is the only productivity number that matters, and it is almost never as large as the pitch suggested, which is itself useful information.
Error rate on the automated step
Count the times the output needed a correction, divided by runs. A draft that needs a rewrite half the time is not saving the hours it looks like it saves; the review pass is the real cost center.
How often the review changes the output
If humans approve without editing, the review is ceremony and can be demoted to a spot check. If they edit every time, the brief is wrong, and no amount of scale will fix it. This ratio is the fastest signal for whether to trust more or brief better.
Measure for four weeks, then decide: keep, adjust the brief, or turn it off. An automation that survives that review, with numbers, is one worth talking about.