Would it be okay to record in the internal records that EAP was provided following the health consultation?

I am in charge of health management at a workplace with 300 employees. Recently, during a health consultation, I guided an employee who complained of both sleep problems and work stress on how to use the in-house EAP.
Health counseling records currently document the consultation date, chief complaint, and guidance/action details. However, I am concerned that if I also record 'EAP guidance,' the HR team or managers might be able to infer whether the employee utilized counseling services later on. Currently, only the health manager has access to the records, but some are summarized and reported during regular inspections. We have not yet shared employee information with the EAP provider and have only provided the employees with the application channels.
At what level should the fact that EAP was provided be recorded? I am wondering if it is better to simply record it as "information on external professional support channels" without verifying whether an actual application was made, and if I need to set separate access rights and retention periods. I would also appreciate your advice on whether it is appropriate to include only the number of notifications in regular reports, rather than individual records.