The initial requirement is to support Amazon Corretto. I have a lot of jar's which are already built by Oracle JDK.
Amazon Corretto is certified using the Java Technical Compatibility Kit (TCK), and It meets the Java SE standard, so should I re-compile all these jars using different JDK (Amazon Corretto 8 in this case)? Does it makes sence?
No there is no need to recompile your Java files into bytecode (class files) when switching between Oracle JDK or Open JDK and Amazon Corretto. If you're switching to a newer JDK then that might be worth investigating, but otherwise Amazon's Corretto is 100% compatible with Oracle and Open JDK.
The Amazon Corretto FAQ has more info: https://aws.amazon.com/corretto/faqs/