Camaldolese

Evangelical Lutheranism also recognizes eremitic life as a form of consecrated life.

And the Camaldolese, a Benedictine offshoot founded by St. Romuald, maintained the eremitic and reclusive tradition into the modern era.

That order matters later in this episode.

But if somebody is looking for a distinct Protestant anchoritic

enclosure tradition, it isn't there.

I couldn't find one, and I looked.

The Camaldolese are Catholic, not a separate denomination.

So the honest answer to the denominational question is...