To add to Bartley's comment, I've been a member of the Guild of One-Name Studies for a few years, and they began the concept back in 1979. A good snapshot is their page describing briefly what a one-name study is in their view: https://one-name.org/one-name-studies/ (though I take some professional exception with the first sentence; in business a project, by definition, is always time-bounded and a study is not). Also, some helpful ONS introductory videos the Guild put together, running from 15 to 40 minutes, can be found here.
I think a Name Study at WikiTree is pretty much whatever the administrator(s) of the study wants it to be. But a one-name study isn't a subset of the genealogy. The study can be--and often is--the superset. More realistically, the better metaphor is probably a Venn diagram. A one-name study could be approached (though I haven't seen one) solely as a population-level investigation, e.g., etymology and first appearances, variant and aberrant spellings, haplotypic DNA information and early origins, migration patterns, localized geographic saturation and distribution over time, and more. You don't need a genealogical tree to address any of those objectives. But most of us get involved in one-name studies because of genealogy.
As Jason noted, the key is scope and defined objectives. And because of that, one-name studies can look very different from each other. I don't think there's a template. When I was planning my initial ONS, a for-purpose website came first, and I had intended to use a PHP/MySQL freeware web application called Webtrees for the collaborative genealogy aspects of the study. Doable, but would have required a whole lot more administrative attention than I could spare. That's why I signed up at WikiTree in the first place: a far better idea for maintaining collaborative family trees associated with the study was a thriving site designed to do exactly that! Sometimes my handful of brain cells don't get in each others' way.
So... Define the scope and prioritize the objectives. Design it from there. There isn't going to be a one-size-fits-all template of an ONS. And WikiTree set-up the Name Studies feature to allow just about all the flexibility anyone would need. I'd say the only thing WikiTree isn't designed to do that was an objective of mine was to house a large asset repository that included a wide variety of elements I wanted to be available only to participants of the study. Currently there are 4 gigabytes worth of stuff in there, ranging from audio files to scans of family bibles. I'm still waiting for someone to upload a digitized 8mm home movie from the 1940s....