Use insert trigger to copy a modified NEW record to another table, with unknown columns
Looks like the underlying issue is that you're trying to pass the row the trigger is acting on as ANYELEMENT, which is for types; what you want here is RECORD.
Assuming you're using PostgreSQL 11 or later (example contains CALL syntax), this should work:
CREATE OR REPLACE FUNCTION increase_trigger()
  RETURNS TRIGGER
  LANGUAGE plpgsql
AS $$
DECLARE
    tbl_out VARCHAR;
BEGIN
    tbl_out := TG_TABLE_NAME || '_increase';
    CALL calc_increase(new, tbl_out);
    RETURN NEW;
END;
$$;

CREATE OR REPLACE PROCEDURE calc_increase(
   sample RECORD,
   tbl_out REGCLASS
)
  LANGUAGE plpgsql
AS $$
BEGIN
    sample.value = sample.value + 1.0;
    EXECUTE FORMAT('INSERT INTO %s VALUES ($1.*)', tbl_out) USING sample;
END;
$$;

Not tested for potential side-effects.