Salesforce Apex API Connection to FHIR Server

I was asked to make an API for Salesforce (SAS) to replace an expensive API Bus software component that is usually used. I used Lightning Web Components for the UI. That uses JavaScript to call Apex (the Salesforce language derived from Java). The Apex code calls the FHIR (Electronic Health Records) API using a library very like RESTSharp. Since it seemed unusual, I am posting the description and working code here. Unfortunately, this needs some background as well because Salesforce is large and seems poorly known. This code is being put here because for all the Salesforce resources out there, code like this wasn't. The learning curve is nasty, but this code is what you get at the end.