Doors – How to remove the rest of this lever-style door handle

I'm trying to remove an old lever-style door handle (with no visible screws) that had a missing latch so was already non-functional. Following online tutorials on how to remove door handles and doorknobs with no visible screws, I made a bunch of progress (even got the plate off, revealing two screws beneath, which I also removed) but cannot, for the life of me, figure out how to remove the rest of the remaining structure.

Photos from different angles (both inside and outside) available here: https://imgur.com/a/2J70dMm

I suspect there's some kind of mechanism that I need to press/engage which will allow me to pull these remaining cylinders and the remaining inner-plate (?) out.

Thanks for your guidance!