My Topology
Two Ubuntu servers, the edge which is exposed to the internet, and the core which is only connected locally. Both are on the same subnet and the core only accepts SSH from the edge server. SSH Private keys are stored on my local computer I'm connecting from. I'm using a custom ssh port and MFA on both servers
What I want to achieve is to connect from my computer to the edge server via SSH and from there connect to the core server using the private SSH key stored locally.
I'm sure it is quite simple but I have no clue how to achieve that.