That said, I think you can still implement integrals or essential b.c. on lower dimension boundaries, however you'll need to do it in separate loops over those boundary elements.

Thank you for the reply and information. I would like to check the suggested method, but is there a way to find these elements after reading the mesh? It seems like information about these regions is omitted when importing the mesh into MFEM, and in my target mesh, the boundary elements are not as simple as in the example, so I need it to be done automatically.

You'll probably need to either modify the reader in MFEM or write your own reader (e.g. based on the one in MFEM) to read and store the lower dimensional boundaries.