This has nothing to do with webflux or servlet. The problem is, that the ObjectMapper config is changed and therefore the output of the actuator endpoints also changed.
In Spring Boot 3 this very unlikely to happen as they introduced a separate ObjectMapper for actuator.
In Spring Boot 2 you have to make sure you do not change the default ObjectMapper, but use a separate one for your business code. Or adjust dependending on some condition, like mime type.
The important thing is that we are talking about the ObjectMapper in your service, not in Spring Boot Admin server. The backend server is just passing through the data it receives.
See also the discussion in the corresponding issue in github: https://github.com/codecentric/spring-boot-admin/issues/3830