More fine-grained alternatives to MeshBase::is_prepared()

[roystgnr]

We have is_prepared() to say that every bit of batch-computed information is up to date, and we have set_isnt_prepared() to manually warn future users that a mesh change has been made that will make some of that cached data invalid ... and we have very little to say that some particular bit of cached data has been invalidated. It's too easy for user code to be left with no recourse beyond "call prepare_for_use() and recompute everything" even when previous code only invalidated a bit.

See idaholab/moose#25378 for a recent such issue.

So ... what do we need to be able to mark and check?

I guess technically we already have clear_point_locator(), so that's one down!

is_partitioned?
has_synced_id_counts?
has_neighbors?
has_elem_data?
has_interior_parents?
has_removed_remote_elements?
has_boundary_id_sets?

Maybe needs_renumbering? Though a mesh never needs renumbering except if it has numbering gaps going into Exodus output; at any prior time renumbering is just for performance reasons...