Hi, thanks for your question at Q&A.
Not being an expert at cognitive services at all I checked the documentation link you supplied and some other sections of the same documentation. In those docs I see it is mentioned "The following table describes the configuration settings supported under the ApplicationInsights section." which kind of leads me to believe the option needs to be declared a little different from you example.
Some of the configuration settings documented in this section of the docs seem to use a Section:ConfigurationSettting
or even a Section:Subsection:ConfigurationSetting
format for the settings. For example Storage:DocumentStore;MongoDB
So i think you should try setting the parameter as ApplicationInsights:InstrumentationKey=<YOURKEY>