ERROR: syntax error at or near "QUERY" QUERY EXECUTE 'set enable_parallel_append = off';

The PL/pgSQL command to execute dynamic query strings is EXECUTE, not QUERY EXECUTE. (Also available in the combined form RETURN QUERY EXECUTE to actually return the results of a dynamic query.)

But this is only one of multiple grave errors in the function. This could work:

CREATE OR REPLACE FUNCTION public.end_to_end_query(part_id integer)
  RETURNS void
  LANGUAGE plpgsql VOLATILE AS
$func$
DECLARE
   _query text := format($x$ALTER TABLE metric_events_%s SET (parallel_workers = 16)$x$, part_id);
BEGIN
   IF part_id IS NULL THEN
      RAISE EXCEPTION 'A notnull part_id must be given!';
   END IF;

   SET enable_parallel_append = off;
   SET work_mem = '1GB';
   SET max_parallel_workers_per_gather = 16;
   -- SET max_worker_processes = 8;  -- double nonsense!

   RAISE NOTICE 'Query: %', _query;
   EXECUTE _query;
END
$func$;

You cannot create a function without declaring the return type, typically with a RETURNS clause. You may want a PROCEDURE instead. See:

• When to use stored procedure / user-defined function?

Double-quotes are not for string literals. See:

• Insert text with single quotes in PostgreSQL

You do not need EXECUTE for plain, static SET commands.

You cannot set max_worker_processes in a function like this. It requires a server restart.

It is nonsense to set max_worker_processes lower than max_parallel_workers_per_gather.

The function is VOLATILE, not IMMUTABLE.

You must defend against NULL input, or the dynamic query string either raises an exception or does something unexpected.

Mixing those general SET commands with setting a table option seems odd. Are you sure, you want to package that in a single function?

When you do configuration chenges isolated to one function, then you should to use syntax like:

CREATE OR REPLACE FUNCTION foo(a int)
RETURNS void AS $$
BEGIN
  RAISE NOTICE '% %', a, current_setting('work_mem');
END
$$ LANGUAGE plpgsql SET work_mem = '20MB';

This syntax ensures scope of configuration change will be limited just by function's execution, and after that, the configuration's changes will be returned back.