It does now occur to me that you could use GPS to determine the height of a point above the center of the earth and, having done so, could use that to establish the location of a pressure sensor. And track the variation of pressure at that known location over decades. So, yeah - I believe that the technology is in being, and probably is in service. That still leaves the issue of selecting the high tide and low tide reading, but . . .
Have a look at Dr Soon discussing why it is not possible to resolve sea level to anything close to the accuracy claimed via satellite. He address is satellites at 17:30