I am struggling with a requirement of having a complete logging mechanizm for both inbound and outbound API calls including the actual request body/header and response body. Outbound is covered by using a custom solution but for inbound where Salesforce standard REST APIs are being called by external systems are unable to log the request/response body. Event logs does give other information like client IDs, timestamps, request sizes etc but not the actual request/response body. How can we log the request/response bodies of the inbound standard salesforce REST API callins?
Event Monitoring (a separately-licensed product from Salesforce) can provide some of the information you're seeking.
This page provides information about the types of events (and the details) that are captured by Event Monitoring: https://developer.salesforce.com/docs/atlas.en-us.object_reference.meta/object_reference/sforce_api_objects_eventlogfile_supportedeventtypes.htm
And here is a knowledge article with some useful links: https://help.salesforce.com/articleView?id=000339868&type=1&mode=1
If this product does not provide enough control over the information you're seeking, you will need to consider creating your own (Apex) API layer that provides that control / level of information.