Do both legs in 220V have to be switched?
Switching both hots is necessary here as you have a two pole relay

Since you have the switch wired as a bypass switch, you need it to have the same number of poles as the thing you're bypassing.  Otherwise, closing the bypass switch wouldn't do anything as the circuit still wouldn't be closed when the relay was open.

If the relay was single pole, your bypass switch could be single pole...

If the relay was a single pole relay that switched one leg/side of the motor circuit, you could use an appropriately rated manual motor controller as a single pole bypass for the relay.  Motor controllers do not need to be all-pole devices as long as they aren't serving as disconnecting means, as per 430.84.

But you may need to get one of those two-pole switches no matter what

If you can't see the breaker box from the pump, then you'll need a two-pole switch, separate from your bypass switch, at the pump anyway to serve as a motor/controller disconnecting means satisfying 430.102 and 430.103. (You'd need this even if the bypass switch was not present!)