With something like this I think you'll want an SQL function.
CREATE TABLE tjson AS SELECT '{
"STATUS":{"1010101010":"1","2020202020":"1"},
"1010101010":"OK",
"2020202020":"OK"
}'::json AS col;
perhaps something like:
CREATE OR REPLACE FUNCTION my_json_valid(json) RETURNS boolean AS $$
SELECT bool_and(coalesce($1->>k = 'OK','f'))
FROM json_object_keys($1->'STATUS') k;
$$ LANGUAGE sql IMMUTABLE;
... but remember that while PostgreSQL will let you modify that function, doing so can cause previously valid rows to become invalid in the table. Never modify this function without dropping the constraint then adding it back again.