What will happen if the MySQL database version 5.7 is deprecated?

Hi, answer to your question is provided in RDS FAQ: it will be automatically upgraded after 3 or 6 month depending on the fact that it is a minor or major version

See https://aws.amazon.com/rds/faqs/

What happens when an Amazon RDS DB engine version is deprecated?

When a minor version of a database engine is deprecated in Amazon RDS, 
we will provide a three (3) month period after the announcement before 
beginning automatic upgrades. At the end of this period, all instances still 
running the deprecated minor version will be scheduled for automatic 
upgrade to the latest supported minor version during their scheduled 
maintenance windows.

When a major version of the database engine is deprecated in Amazon RDS, 
we will provide a minimum six (6) month period after the announcement of 
a deprecation for you to initiate an upgrade to a supported major version.
 At the end of this period, an automatic upgrade to the next major version 
will be applied to any instances still running the deprecated version during 
their scheduled maintenance windows.

Hope it helps

Didier

If the version of RDS is no longer supported by AWS, it will be updated automatically.
When that happens, AWS will basically contact you and you need to find out the impact and fix it before it is automatically updated.

The following URL is a guide to the end of support for MySQL 5.6.
Thus, when support expires, updates are automatically initiated.
https://repost.aws/questions/QUdbXvmqLGTkC8kdmB_Vc3Bg?annID=8790

• Starting March 1, 2022, Amazon RDS will begin automatically upgrading MySQL 5.6 instances to version 5.7. If a customer restores MySQL 5.6 database snapshots, Amazon RDS will automatically upgrade the restored database to MySQL 5.7.