In the cloud everything costs.

What Azure will offer you is this: 

 - Build in the cloud with an [Azure free account][1]: they will give you around $200 for free. Then you pay.
 - If you use Azure SQL Database `Basic` or `S0` you will have contained costs at least at the beginning with bad performances. 
 - Azure SQL Database [Serverless][2]: your database will go to sleep after 1h of no connections. But you will pay a bit more when in use. 

You cannot escape the costs when you are in the cloud. 

Maybe try to put everything on a NAS at home if it's an amateur project. 

EDIT: There is also this new cloud which is apparently very cheap: https://neon.tech/

  [1]: https://azure.microsoft.com/en-us/free
  [2]: https://learn.microsoft.com/en-us/azure/azure-sql/database/serverless-tier-overview?view=azuresql&tabs=general-purpose