How to use psql, plpgsql and session variables together in one file

vars.sql

-- psql variables can only be used outside functions 
-- plpgsql variables can only be used inside functions
-- session variables can be used both outside and inside functions, bridging the gap between the two types of variables
\set func_name vars
\echo '[':func_name'.sql]'

CREATE OR REPLACE FUNCTION :func_name (arg_execute TEXT)
RETURNS VOID AS $$ DECLARE
BEGIN
END;
$$ LANGUAGE plpgsql;

SET SESSION skylab.func_string TO :'func_name'; -- transferring a psql variable into a session variable
SELECT * FROM plpgsql_check_function(current_setting('skylab.func_string')) AS errors;
DO $$ BEGIN
    IF (SELECT COUNT(*) FROM plpgsql_check_function_tb(current_setting('skylab.func_string'))) > 0 THEN -- and then transferring the session variable into plpgsql
        RAISE EXCEPTION '%', current_setting('skylab.func_string');
    END IF;
END $$;
SELECT :func_name('execute');