What is the term for a hedge-covered pathway?

It is called a pleached tunnel or a pleached allee. See Gardening Knowhow, article titled What Is Pleaching: Tips On Pleaching Hedges And Trees. See also Images for Pleached Tunnel.

Landscape Architects Network. Photo credit: Pleached allee, Glen Burnie Historic Home ... Architectural Photographer: Ron Blunt (ronbluntphoto.com)

The article is an introduction on how to pleach trees. It starts:

Pleached trees, also called espaliered trees, are used to create arbors, tunnels and arches as well as the “hedge on stilts” look.

The article concludes:

Arbors and tunnels retain the framework permanently. If you are creating a pleached tunnel, be sure it is tall enough that you will be able to pass through it once the pleaching technique spreads the branches onto the support.

Arborway: an arbored passage or walk.

Arbor: a shelter of vines or branches or of latticework covered with climbing shrubs or vines.