How to tighten a door handle with no visible screws or holes
The "inside" handle (on the right in the last/lower picture) will have a small spring-loaded button on the handle post (the part you don't put your hand on when opening/closing). Use an awl or equivalent tool to depress the button and remove the inside handle. Then unscrew the inside trim ring (lefty/loosey) to expose the screws that hold the whole assembly together. Tighten em up and put er back together.