Please upgrade to ApplicationInsights-JS@^2.0.0. It now has Fetch instrumentation which is based on the code of this package.
Fetch API monitor for Application Insights
The monitor is based on official Ajax Monitor and mostly replicates what was done there for fetch function.
npm i --save applicationinsights-js @types/applicationinsights-js application-insights-fetch-monitor
import { initAppInsightsFetchMonitor } from "application-insights-fetch-monitor";
appInsights.downloadAndSetup({ instrumentationKey: "[YOUR INSTRUMENTATION KEY]" });
initAppInsightsFetchMonitor();