Hi @Steve Hawes ,
Microsoft offers detailed information about compliance offerings of Azure Services here: https://azure.microsoft.com/en-us/resources/microsoft-azure-compliance-offerings/
Maybe this official and public available document is helpful for your ISO 27001 ISMS: https://azure.microsoft.com/mediahandler/files/resourcefiles/microsoft-azure-compliance-offerings/Microsoft%20Azure%20Compliance%20Offerings.pdf
You will find these details for Azure Database for PostgreSQL in the document
In the same document starting on page 7 is a paragraph related to ISO 27001 with a link to the audit report and certificate.
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Regards
Andreas Baumgarten