A couple of thoughts here.
First, there is a decent amount of the bacteria we want which lives in the substrate. In an unplanted tank the oxygen level in the substrate tends to be too low to support tje bacteria somewhere much below 1/2 inch and by an inch it is too low. So how much additional substrate one puts into an established tank can matter over the short term. So it makes sense not to completely cover the exusting substrate with over about 2/3 of an inch of new.
One way to avoid this kind of an issue it to add the new substrate over time so that you are not completely losing the substrate bacteria for any amount of time.
Next, a planted substrate is one of the best filters there is. This can be even better if one has snails or fish which burrow as this helps oxygenate the substrate. Moreover, some plants whose roots are in anaerobic zones will transport oxygen down to their roots where they release it. The result is that the nitrifiers can now live there and ammonia gets more easily created. The plants want tha ammonia (as NH4 ammonium). Additionally, because the bacteria down there are creating nitrate, within the anaerobic zones around the oxygenated ones denitrifying bacteria colonize. The result is the nitrifying and denitrifying zones are basically coupled and work together and the plants benefit.
So as to how to add new sand to a tank filled with water. I have tried the cup method and it works with small amounts but is hard if one want to raise the level over a decent area through a decent depth of water. Further, the new sand is dry and once the cup is wet the sand behaves a bit differently. I came up with what I consider is a better method for adding dry sand to a filled tank.
I have a variety of gravel vacs. The ones for use in bigger tanks have a fairly lone tube that is also 1.5 - 2 inch diameter. I pour dry sane into the top of the tube which is above the surface and it slides out the bottom of the tube pretty close to where it is supposed to land. Not only can I control where the sand lands by where the bottom of the tube is, but I can also easily control the volume of sand being placed there. I simply pour the sand faster or slower.
The fun part of this is how some of the fish react. They can see the sand but not the clear tube. They also tend to react to the sand as if it might be food. The result is some bump into the tube trying to grab a gain of sand.