How to set up a spring-boot application with java 13

You should migrate to using spring-boot 2.2.0 which includes the migration to using Spring Framework 5.2.0 which extends supports until Java-14.

Reference - Spring-Framework-Versions#jdk-version-range

Here are the Draft Release Notes for further information and references and the current version to test this out would be 2.2.0-RC1.