Hi,
The Serverless tier of Azure SQL Database (this is what the Free offer provides) is for when you only need to use the database for a relatively small total number of hours each month. Based on your description you need the database to be available 24x7, so the free offer isn't a good fit.
I would recommend you create a new Azure SQL Database and this time select DTU purchasing model, Standard tier, and 10 DTUs maximum. This will give you a fixed monthly cost for the database (you will see the cost for your region before you Create it).
Once you have this new database up and running you will need to test with your specific workload and data to see if 10 DTUs is enough. If it isn't performing and the cause is due to not enough resources, you can easily increase the number of DTUs at an increased monthly cost.
At a certain point in the future when you have more experience with usage of your application and what it requires (in terms of database) you may want to switch to vCore model.
As far as the free database offer, I suggest you keep it as it is, and then when the vCore seconds resets in the next billing period you can use it only for brief experiments/testing, since it is free. I DO NOT recommend you select "Continue using database for additional charges" since that will likely result in a large bill.
Azure SQL Database pricing
https://azure.microsoft.com/en-us/pricing/details/azure-sql-database/single/
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Thanks.
-TP