The current behavior is:

julia> (sin ∘ missing) == (sin ∘ missing)
true

But it seems like we should actually have == return missing in this case? This is because missing basically represents a wildcard function here, the way I interpret it at least. This would be analogous to, e.g.:

julia> (missing, 3) == (missing, 3)
missing

This is a special case to consider for #53853.

Not sure if I should label this for triage, but it'd be nice to get a quick decision here, given that it's relevant to @jw3126's PR #54877.