Mortar mesh generation failed when a mortar boundary has coincident/overlaid nodes

[hugary1995]

Bug Description

I managed to reproduce this error with a very simple MOOSE-only input file. This is a 2x2 element mesh.
The top half and the bottom half of the mesh are NOT connected, i.e. there are four nodes on the left and right boundaries, respectively.

When I apply a mortar constraint on the left/right boundaries (and their respective lower dimensional blocks), I get an error saying:

Could not associate primary/secondary neighbors on either side of secondary_node.

which comes from AutomaticMortarGeneration.

Steps to Reproduce

[Mesh]
  [top]
    type = GeneratedMeshGenerator
    dim = 2
    ymin = 0.5
    ymax = 1
    nx = 2
    ny = 1
    subdomain_ids = '0 0'
  []
  [bottom]
    type = GeneratedMeshGenerator
    dim = 2
    ymin = 0
    ymax = 0.5
    nx = 2
    ny = 1
    subdomain_ids = '1 1'
  []
  [combine]
    type = CombinerGenerator
    inputs = 'top bottom'
  []
  [pin]
    type = ParsedGenerateSideset
    input = combine
    new_sideset_name = pin
    combinatorial_geometry = 'x>0.499 & x<0.501'
  []
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    input = pin
    sidesets = left
    new_block_id = 11
    new_block_name = secondary
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    input = secondary
    sidesets = right
    new_block_id = 12
    new_block_name = primary
  []
[]

[Problem]
  solve = false
[]

[Variables]
  [u]
  []
[]

[Constraints]
  [mortar]
    type = PenaltyEqualValueConstraint
    secondary_variable = u
    primary_boundary = right
    secondary_boundary = left
    primary_subdomain = 12
    secondary_subdomain = 11
    penalty_value = 10
  []
[]

[Executioner]
  type = Transient
  num_steps = 1
[]

Impact

This prevents me from running simulation with discontinuous mesh (discontinuous as in blocks are broken by duplicating nodes). If the boundaries are not conforming, however, it seems that I can bypass this error message, but the Jacobian is sometimes singular.