Should `.below` be marked as private/internal?

See for example

#check List.Sublist.below.cons
List.Sublist.below.cons.{u_1} {α : Type u_1} :
  ∀ {motive : (a a_1 : List α) → a.Sublist a_1 → Prop} {l₁ l₂ : List α} (a : α) {a_1 : l₁.Sublist l₂},
    a_1.below → motive l₁ l₂ a_1 → ⋯.below

In tests/lean/run/constructor_as_variable.lean we now see the error:

error: invalid pattern, constructor or constant marked with '[match_pattern]' expected

Suggestions: 'List.Sublist.below.cons', 'List.Sublist.cons', 'List.cons'

on the test

def ctorSuggestion2 (list : List α) : Nat :=
  match list with
  | nil => 0
  | cons x xs => 1 + ctorSuggestion2 xs

These .below auxiliary functions are rarely (never?) meant to be used by users, and perhaps should be marked as private or internal in some way, so they would not be displayed here.

There is already a check for isPrivateName when generating this message.

Read src/Lean/Elab/PatternVar.lean, especially the existing isPrivateName check, and reproduce the diagnostic with tests/lean/run/constructor_as_variable.lean. Determine how the .below auxiliary functions should be classified, then verify that constructor suggestions no longer display them while retaining useful suggestions such as List.cons.