Hibernate is supported, I don't know how about Jackson. Application will not be affected even if it is not supported. You may not see full details about statement preparations in purepath, that's all.
The OneAgent supports java in general. A framework does not have to be on the supported list in order to guarantee it to be working. Things on our supported list are there because we have an specific feature for it.
From that perspective any java library and java package is safe to be used with OneAgent.