Option 1: Cheap fix, toggle bolt the railing in.

Option 2: Cheap fix. Since the hole is 1”. Slide a piece of 1” lumber in and you can screw directly to that which will sandwich the plasterboard between the railing and 1” wide lumber.

Option 3: Move the railing completely to where it screws into studs.

Option 4: Cut out a section of wall and put a wooden brace in between the studs. Then repair the cut out section and screw railing into the brace.

Options 3 and 4 will last the longest.