How to list all functions with arguments that a role is allowed to execute in Postgres?
You can use the has_function_privilege function for that:

SELECT p.pronamespace::regnamespace as schema,
       p.proname||'('||pg_get_function_arguments(p.oid)||')' as function
FROM pg_proc p 
WHERE has_function_privilege(p.oid, 'execute');
  and p.pronamespace &lt;&gt; 'pg_catalog'::regnamespace;