I have been thinking how MemberQ is a sort of special case of MatchQ. MemberQ assumes a list, rather than simply a pattern, as MatchQ does -- as its second argument. For example:

MemberQ[{a, b}, a]
MatchQ[{a, b}, {___, a, ___}]
MatchQ[{a, b}, {___, ___, a, ___, ___}]
MatchQ[{a, b}, List[___, a, ___]]
MatchQ[{a, b}, List[___, ___, a, ___, ___]]

(* OUTPUT: *)
(* True *)
(* True *)
(* True *)
(* True *)
(* True *)

Is there any way to write the pattern in MatchQ without explicitly specifying the List? I'm thinking of something like the following: MatchQ[{a, b}, ___ ~~ a ~~ ___]

...but that's incorrect syntax (and returns False) because the use of ~~ implies a StringExpression, and {a, b} is clearly not a StringExpression. So, how can I write a pattern representing "any subexpression containing the symbol a anywhere"?

I could accomplish this using the resource function ContainsQ:

ResourceFunction["ContainsQ"][{a, b}, a]

(* OUTPUT: *)
(* True *)

But what is the built-in way to do this?

Looking at the source notebook for the resource function ContainsQ, I see that the definition of ContainsQ is simply:

ContainsQ[args___] := (Needs["GeneralUtilities`"]; GeneralUtilities`ContainsQ[args])