A search of "empirical grounding" in my small personal article database showed more results in test validation than in qualitative (though this could be a personal bias: I'd be curious what kinds of articles your search brought up). Searching this term in the university database brings up a large variety of results, really highlighting the diversity of the use of the term (from policy to measurement).
Additionally, a reading of the Eisenhardt and Graebner article makes it clear to me that their definition of "empirical grounding" is primarily focused on the thought that the theory is grounded in the data, and not as its own distinct methodology. In their sense, this could be viewed as an aspect of grounded theory (when done correctly, it is grounded in data).
Based on this, I would say that empirical grounding is not its own method (or, if it is, certainly not a standard/well-known method). To address the second part, I do think that the term has meaning independent of grounded theory: specifically, as its name implies, it is the practice of grounding theory/methods/conclusions within data (and this has a range of applications). In my understanding, "empirical grounding" is almost an epistemology in terms of its practice and scope. Thus it could, in the larger sense, be considered a broad methodology, under which traditional grounded theory (and perhaps all of quantitative) could fall.
I did find the below article that discussed the broadening of grounded theory from "empirical grounding". They, however, seem to come to this term merely by similar processes as Eisenhardt and Graebner (simply trying to communicate that the method is grounded in data) and do not seem to view it as its own proper method or name.
Goldkuhl, G., & Stefan, C. (2010). Adding Theoretical Grounding to Grounded Theory: Toward Multi-Grounded Theory. International Journal Of Qualitative Methods, 9(2), 187-205.
In example of the multiple uses, below is an article where Messick uses "empirical grounding" to mean "trustworthiness" regarding score interpretation (a pretty well known article and author in the measurement sphere).
Messick, S. (1980). Test validity and the ethics of assessment. American Psychologist, 35(11), 1012–1027. https://doi.org/10.1037/0003-066X.35.11.1012
All in all, for the purposes of your question: no, it doesn't appear that this is a well known or accepted methodology distinct from grounded theory. It seems to have many definitions in many contexts. Based on the Eisenhardt and Graebner article, it seems to a desirable outcome of a grounded theory. Based on definitions in the Goldkuhl and Stefan article, it is a piece of multi-grounded theory (and appears to capture the goals of traditional grounded theory).
