I've always had an understanding that almost all of the water pumped from underground is replaced by seepage from rain, snow and surface water. I know of a home in CA that gets its water from a well which has been at the same level for over 20 years, strongly arguing for seepage replacement.
People do pump what is called "fossil water" which apparently is not replaced, causing wells to run dry. Such stories have been seriously rare except in unusual places like the Ogallala Aquifer, also mentioned in the article, where replacement appears to be substantially less than loss.
Can such places contribute non-trivial amounts to sea levels? The article reports research to be published which alleges this is true.