As far as I know, yes, this is an expected behavior. The web part of the document library does not show the breadcrumb if you are traversing through nested folders. When you click on the Folder in the web part, the web part refreshes and opens the child
folders/documents. But I do not see a way of going back to parent folder from here.
Regards, Kapil ***Please mark answer as Helpful or Answered after consideration***