You are looking at pictures of the “attic” space a flat roof urban rehab. House has serious energy bills and air leaks (measured with a blower door). The roof joist are maybe 3×12 with r30 batts poorly installed. The ceiling is a dropped sheet rock, hung from metal channels , but there is only access from the area where the photos were taken.
Since the roof insulation is too little and of a poor install, I am recommending blown cellulose as least disruptive most cost effective solution. The can lights are 20 years old and area most likely no IC rated, so airtite IC retrofits would have to be installed.