Start from the fact that a green status page and a real outage are entirely compatible, and understanding why tells you what to measure.
Status pages are typically updated by a human after an incident is declared, against thresholds set by the vendor. Most real-world degradations never cross those thresholds because they are partial: one region, one data centre, one endpoint, one customer tier, or a percentage of requests. A fifth of your requests failing is a textbook partial, and a vendor whose global error rate moved by a fraction of a percent will show green and mean it.
Which also explains "we are not seeing any issues" — they are probably looking at an aggregate, and you are a rounding error in it.
So the shape of the evidence you need is specific enough to look up, not statistical. What actually gets acted on:
- Request ids or trace ids from the failed calls. Most APIs return one in a response header even on errors, and this is the single most valuable thing you can hand over — it lets them find your exact request in their logs rather than looking at a graph.
- Exact timestamps with the timezone stated.
- The precise endpoint and method. Partial outages are often one endpoint.
- Your source region, because regional is the most common shape.
One ticket with ten request ids beats twenty messages describing a percentage.