What is the meaning of this symbol (long vertical arrow) in old organ notation?
It indicates which staves the registration instruction apply to.
But in fact your particular example seems confusing, because it indicates different stops for the two manual staves, even though the arrows link them together. And it doesn't make much practical sense to have the solo played on a single 4' flute (sounding an octave higher than written) accompanied by three stops which together would probably be too loud.
If the registrations were intended for a typical small 19th century English organ, it probably means two diapasons (open 8' and stopped 8') plus oboe 8' on the swell for the left hand, with the 4' flute on the great coupled to the swell for the right hand.
More modern notation often uses brackets instead of arrows.