What iOS apps read health records from Apple Health?
Here's an app that appears to match: ClinicQ by Health Here.
The fourth screenshot on the AppStore claims:

CliniQ can import your allergies, medical conditions, procedures and medications from Apple Health


In the process, I found how to add an institution as a data source (Apple Health can pull records from a compatible portal) although this is not yet enabled in Australia, probably because currently only US, UK and Canada have participating sources.
I also learned the difference between Health Records and the older Clinical Documents.
Finding apps that DO NOT access Health Records was quite easy.  For Aussies, the Healthi app can connect to MyHealthRecord records, but doesn't integrate with Apple's Health app.
Around launch time (2018), A tale of two hospitals mentions Johns Hopkins and Penn Medicine as early adopters.  The same article mentions 'EMR vendors such as EPIC, Cerner, Athenahealth, Meditech and AllScripts'... these are potential sources for more examples of apps that DO use the Health Records.