Feature Request: SQL in SQL prettification

Describe the Feature

I want formatting of SQL inside function bodies written in quoted stings

Why do you want this feature?

If you are writing SQL functions, it's pretty common to have SQL embedded inside SQL; for example (straight out of Postgres documentation):

CREATE FUNCTION dup(int) RETURNS dup_result
    AS $$ SELECT $1, CAST($1 AS text) || ' is text' $$
    LANGUAGE SQL;

In this case, $$ is a string quoting delimiter, and SELECT $1, CAST($1 AS text) || ' is text' is a quoted string.

The issue is that most SQL formatters do not recurse into these quoted string function bodies, so the function declaration is prettified but the function implementation remains ugly. Here's what I get if I run the above through prettier with prettier-plugin-sql:

create function dup (int) returns dup_result as $$ SELECT $1, CAST($1 AS text) || ' is text' $$ language sql;

What I wish I got would be more like

create function dup (int) returns dup_result as $$ 
    select
        $1,
        cast($1 as text)||' is text'
$$ language sql;

(Which is what I get if I manually run the function body through prettier-plugin-sql and then paste it inside $$ delimiters.)

No file, test, or entry point is named. Start by locating the formatter's handling of quoted string delimiters and SQL function bodies, then determine how nested SQL should be parsed and formatted; done means the PostgreSQL example produces formatted SQL inside $$ delimiters without changing the surrounding declaration.