An Azure managed MySQL database service for app development and deployment.
This is not a vCore quota error. Microsoft documents that program subscriptions, including Sponsorship and Microsoft for Startups offers, can have a limited set of regions for MySQL Flexible Server, and regional capacity can further restrict a subscription.
First confirm the Microsoft.DBforMySQL resource provider is registered under Subscriptions > Resource providers. You can also run az mysql flexible-server list-skus --location uksouth -o table for each region. That shows available SKUs, but it does not guarantee your sponsorship subscription is entitled to deploy there.
Because the same error appears in several regions, open an Azure support request using Service and subscription limits (quotas), select Azure Database for MySQL Flexible Server, then request Region access. Include the subscription ID, target region, SKU, vCore count, HA/zone choice, failed deployment timestamp, and correlation ID. Requests are reviewed against capacity and are not guaranteed. Meanwhile, test an alternate region or smaller SKU without zone-redundant HA.