Please check this screenshots , I have done for thor user password less authentication for stapp01,stapp02 and stapp03
You have to do passwordless ssh in app server with their respective sudo user but you did without specifying sudo user.
thor --> jump_host
tony --> stapp01
steve --> stapp02
banner --> stapp03
thor@jump_host /$: ssh tony@stapp01 Last login: Mon Jun ....