these images show the setup of categories and the answer, see how the ESP8266 Module entry is a child in one and not a child in the other?
Please use 2.4.5 from Github, I am sure that will solve all ajax issue.
You args should be: [anspress categories="ans-esp8266-module"]
Never tried bbPress with AnsPress. Will have a look.
Yes it was not pushed to WordPress. 2.5 will be pushed directly to WordPress.org