I assume that you executed your API, after configuring the Log Invocation policy to store payload. If not, events are obviously not generated.
I’m providing a complete answer for everyone’s benefit, beyond just the payload data that you need to view -
Analytics - API Gateway is configured as the default destination for events. You will be able to see the events and metrics under Analytics. Now, Analytics is available a 2 levels - Gateway and API. This is documented here (link), or in chapter 11 of the user guide, if you’re using the PDF version (link).
Elasticsearch & Kibana - API GW uses Elasticsearch for storage (including payloads), which you can access via both API GW UIs or access Kibana directly if you know what you are doing. You can customize the views as well.
Destinations - In addition, you can add more destinations for events, apart from API GW. Various destination options are available under Administration. Required destinations must be configured here, before you use in your policies.
Programmatic Access - API GW also provides you REST APIs to the analytics store that you can use for, say, billing.
Payload - You will find this under API Analytics (open your API and then the Analytics tab). Apply your duration filter and then scroll down to Runtime events and expand your Transactional event entry; you should see 2 items for request and response payloads.
You should see the payloads -