The fundamental problem with complex phenomena is in defining the domain(s) of interest.
If we want to talk about the total amount of H2O around, on, or in the Earth then inclusion makes sense.
If we want to talk about water interacting with the surface environment (atmospheric, sea, ice cap, fresh, and subsurface aquifers and tectonic water), then splitting those into distinct categories probably also makes sense. In which case we can also show the subsurface water.
How much mantle water does make it to the surface over time is a good question. I've no idea though I'd suspect that some does through geothermal and tectonic activity. The more interesting question might be how we'd determine this (all but certainly through isotopic composition), and if a net flux could be determined.
Over geological time, additional reservoirs of water are significant simply because surface water boils off into space over time, with estimates I've seen of up to 25% of Earth's original allotment having done so over 4.5 billion years or so. As the Sun eventually grows warmer, this rate will increase. At the same time, tectonic activity will slow.
Note that there's a fair bit of water transport through the lower crust / upper mantle as oceanic plates subduct under continental plates, with the water absorbed into the oceanic plates playing a major role in volcanism at those plate boundaries, e.g., along the "Rim of Fire" surrounding the Pacific basin.