Use a baseline for every request
For each request, record what it would have cost at the model and prompt your app originally used, priced with the provider's published rates. That is the baseline.
Record the actual cost
Next to the baseline, record what your provider actually charged for the same request. Together the two numbers show the result of every single request.
Savings are the difference
Verified savings are the baseline minus the actual cost, added up for the month. Because the figures come from individual requests, you can sample any of them and recalculate by hand.
Report by business dimensions
Break the total down by app, by provider and by week. Each team then sees its own result, and unusual weeks stand out.
Keep the data exportable
If you cannot export the request-level data, you cannot audit the result. Insist on a file you can recalculate with your own price list.
Why it matters
A saving you can check is a saving you can budget on. That is the standard we hold PromptPinch to: every invoice shows the baseline, the actual cost and the difference.