System Overview Page reflects messages when the user reaches 95% of limit.API Usage section displays API request usage details up to last 24 hours.
Company Information Page displays usage dependent API request limit per month. It is helpful in reflecting org’s API calls aggregate up to 30 days.
To get Bulk API Limit requests, SOAP API requests, and Streaming API limits consider using OrgLimits class in Apex.
Resort to Limits REST API to get all information related to limits that includes APIs.
The responses can be saved/used as per the limit that needs to be explored.