Russell Thanks for posting your question in Microsoft Q&A.
#1 I think you are referring to Recover a deleted storage account doc about 14 days. You may be able to recover the deleted storage account within 14 days by the following instructions in the doc. However, this is not same as deleting the storage account and trying to recreate it with the same name.
For both storage account and API Management scenarios (even after purging), this is due to Prevent dangling DNS entries and avoid subdomain takeover and this feature from Azure Name Reservation services ties the service name to the customer's subscription (for a cool off period). Here is similar discussion and you can wait for the cool off period (Enterprise subscription - 180 days, non-enterprise subscription in general - 7 days (some: 30 days)) for the name to be available again. Check out Identify dangling DNS entries doc to get all DNS entries for a subscription/tenant.
If you need immediate help and can verify both subscriptions belong to the same owner, reach out to azure support team and they can further assist you with that. I hope this helps and let me know if you have any questions.
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