Those look like they are in the upper drive bays.
OP can take another picture from an angle. The lower 3.5 drive bay looks recessed from the upper 5.25 bays.
How is the lower bay attached to the upper bay?
Remove your new drive and see if the lower bay is held in place by sliding clip...in which case, try to move the lower cage right and see if the entire cage comes out before you can access the drive.
Think of the cage like how your case cover slides on..maybe a set screw to keep it from sliding off as well.