Hello Grant Moran,
Welcome to the Microsoft Q&A and thank you for posting your questions here.
I understand that your Postgres Flexible Server stuck in "Updating" for 24+ hrs during GP to Burstable scale-down (ServerIsBusy on retry).
This is not a PostgreSQL engine, extension, HA, replica, query, or configuration issue. It is an Azure control-plane/provisioning issue. Azure PostgreSQL Flexible Server supports compute scaling, but the operation is expected to complete through the service-managed scale/restart workflow, not remain in Updating for 24+ hours.
Since PCS is already handling the case, request Azure Database for PostgreSQL Flexible Server backend intervention to clear, complete, or safely roll back the stuck provisioning operation. Do not keep retrying scale, restart, stop/start, or generic ARM update operations, because ServerIsBusy means the server is already locked by another operation and customer-side retries will not clear it. - https://docs.azure.cn/en-us/postgresql/configure-maintain/how-to-restart-server
If the Azure portal support flow is blocked or the Next button is greyed out, create the support request using Azure CLI or Azure Support REST API. - https://learn.microsoft.com/cli/azure/support/in-subscription/tickets and https://learn.microsoft.com/en-us/azure/azure-portal/supportability/how-to-create-azure-support-request,
I hope this is helpful. Please! Do not hesitate to let me know if you have any other questions, steps or clarifications.
Please do not close the thread by upvoting and accepting the answer if any part of it is helpful.