Expert level is walking on top! (Sorry—I couldn't resist.)
What you have seen on YouTube is typical, but there is no ‘correct’ or ‘incorrect’ depth at which to walk.
There are two general purposes for walking in water: first, to use the buoyancy of the body to remove part of the load from the joints, and second, to add resistance to movement through dynamic fluid pressure. The deeper the water, the greater the buoyancy, and hence the lower the load on your joints. But the greater the buoyancy, the less friction there is between your feet and the bottom of the pool; and the deeper the water, the greater the resistance to movement. Thus, as the water becomes deeper, there is greater resistance to motion, but you are less able to overcome it. This is, of course, why you have difficulty walking at the deeper end of the pool.
Buoyancy varies greatly from individual to individual, as a function of body composition. Fat is less dense than water, so it helps us float; muscle and bone are denser than water, so they contribute to our sinking. We consequently all have different degrees of buoyancy. Thus, the ‘right’ depth comes down to the individual, and to fitness for purpose, as always. You want to wade in a depth that alleviates your joints as much as you need, whilst offering enough resistance to work your heart and muscles to an extent that you are receiving a training effect.
Waist-height (or slightly above) is often a good height, since you can usually maintain a good purchase on the bottom of the pool, whilst being subject to a reasonably high resistance that keeps you working. If it feels too easy or difficult, you can simply adjust your depth as necessary. (If possible, working across the pool at the same depth is preferable.)
As an addendum, is is worth noting that although the buoyancy of the water relieves the joints, it also places greater load on your heart in the form of increased blood pressure and venous return. For this reason, shallower depths are preferable if you have any kind of cardiac or cardiovascular condition.
I hope that helps.