Mesh is unexpectedly unprepared after (or before?) stitching

[roystgnr]

I don't have time to look deeply into idaholab/moose#32390 (comment) soon, and we don't want to hold up that PR on it, but it may be a bug we need to fix in libMesh and even in the best case scenario it points to something we need to be more careful about in MOOSE.