The measurements themselves are not anything like so accurate. The ways people take the measurements depend on the needs and the facilities available. They vary from marked posts standing in the water, through buoys that can be surveyed to see how high the water floats them, up to satellite observations of the height of the water.

All those methods produce errors and uncertainties far greater than a few millimetres, and even if they didn't, there are major variations in water depths at any particular point from time to time. Buoys can have layers of salt, fouling, or moisture that change the depth at which they float, apart from questions of temperature for example. It takes a very moderate breeze to affect water depth, and tidal forces and invisibly small storm surges from many thousands of kilometres away change the readings.

The figures you read that are accurate to a few centimetres or less, are derived by mathematical smoothing of data spread over long periods and large areas. If they are competently derived and competently applied, they are meaningful and useful. If they are taken too simplistically, or without regard for their proper statistical limits of confidence, they amount to simple delusions of accuracy.

In any case, suppose that all the work has been properly done and all the statistics are properly applied and all the presentations honestly and competently prepared, then when you come down to it, what does a difference in depth of say 3 mm mean in practice? Is it important? Well yes, it can be, but one really needs to understand the nature of its importance, and the importance of the uncertainties that need to be resolved before one draws conclusions. For example suppose the top hundred meters of water depth has warmed up by a few degrees: that could easily cause a difference of 3 mm. Does that matter? It might well. That would represent a huge amount of heat, even if you would not notice the difference in temperature by putting your hand into the water. Suppose the difference resulted from say glacial melting; does that mean that a single island or jetty will be put at risk by 3 mm? No, but do a little arithmetic and ask yourself how much water would have to melt off the glaciers to raise the depth of even the North Atlantic by 3 mm.

Your question deals with huge matters of a huge complexity with huge significance. Unfortunately it also deals with conflicting political interests and prejudices that have made such a mockery of the results and debates that have been presented, that you cannot trust a thing you read on any side of any debate without considerable suspicion and patience in evaluating what you hear or read.

Bottom line: keep alert, keep asking, keep thinking, keep remembering, and see what emerges.

Go well,

Jon