Dead bug is a dynamic lumbar (low back) stabilizing exercise, which means the main goal is to keep the spine neutral despite shifts in torque caused by the big arm and leg movements. Sending the center of mass of one leg or both away from your core may cause your pelvis to tilt forward, and extending your arms overhead may cause your rib cage to tilt back, and both of these movements make your lower back arch. The goal in dead bug is to keep the core constantly contracted to maintain a neutral pelvis, low back, and rib cage. It's pretty subtle: you want to maintain a position like A in the image below, and avoid a position like C.
It doesn't matter exactly what your arms and legs are doing in dead bug, as long as you do a variation that's easy enough that you can keep your low back pressed into the floor. With all else equal, I'd say the easiest option is to have one foot on the floor with the knee bent while the other one lowers (first option from the second video), because in that position, the bent leg helps support the neutral position of the pelvis. The medium option is to have one leg straight up above the hips while the other one lowers (second option from the second video), because the leg that is up is stacked straight above the pelvis so it doesn't contribute much forward-tilting torque to the pelvis. The hardest option is to have one knee bent at 90-90 while the other lowers (first video), because now both legs are contributing to forward-tilting torque on the pelvis. You have to keep the bent knee above the hips though, if you bring it in toward the chest you lose that torque. In any of these positions, only lower the leg down as far as you can keep the lower back pressed into the floor.
If you can do all of these variations without arching your back at all, the next step up is to do exercises in which you lower both legs, such as this one. In this video they add another variation you can incorporate into dead bug with the head and shoulder lifted. This engages the upper abs, and helps keep the rib cage in a neutral position, which in turn prevents the low back from arching.