The sea level is accurately me&sured on a routine basis using satellite accurate altimeters, mainly baed upon maicrowave cohernt techniques. By reteitive obesrvations, one can rech an acci uracy of about 1 or 2 millimataers. These satellite data can be assimilated with buoys on the "graound". . This is the way how official IPCC reports are built.
Sea level rise is mainly due to rwo additive phenomena: natural dilataion due to temperature rise and melting is Earth surface glaciers and snowcaps. Te ratio is about 50-50 but this point can evolve slowly with time and iqs still under scientific discussion. Anyway, the two imacts are due to temperature rise.
I forgot to explain that the footprint of the microwave sounder should be large enough to fileter the local impact of waves and get a meningful local mean sea level. Actuamlly, this is a natural result of both theoretical and technological e reasons. The first sounders were developed by NASA (US), CNES (France) and ESA (EU). Japan brought also a contribution of its own. Worldwide satellite and ground altimeters and buoys are collected in a coherent way, more or less like meteorological data by WWO.
There are altimeter satellites. they measure sea level relative to the shape of the geoid. these data can be used to obtain information about the lowering or rising of the water level at any point in the ocean. The change in the height of the level at a particular point depends not only on the melting of ice during warming. the water level changes when the gravitational field changes, for example. thus, it is necessary to additionally take into account changes in the gravitational field. For this, a satellite program has been created. However, it is usually not the rise in the level of the ocean that is of interest, but the process of flooding the land by the ocean. for this, a satellite program for land radar using a synthetic aperture was created and permanent geodetic networks were created.
You are perfectly right, but do not forget one important component, which is water thermal dilatation. As we all know, this classical phenomenon can be évidence even with a very simple lab material. . Actually, beyons other causes, sea level rise under cliamte change is due both to thermal dilatation and semlt of terrestrial glaciers. The effect that you underline is true also, needless to say.